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Elimination Method Mean in Math?

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The elimination method using solving a system of linear equations algebraically is the most widely used method out of all the methods to solve linear equations.

 In the elimination method, we eliminate any one of the unknown variables by using basic arithmetic operations and then simplify the equation to find the value of the other unknown variable. Then we can put that value in any of the equations to find the value of the variable eliminated.

The elimination method is very simple and easy to use because here we eliminate one of the terms that make our calculations simple. In this article, we will learn to solve the systems of linear equations by using the elimination method. We shall solve various examples based on the concept for a better understanding.

What is an Elimination Method?

 The definition of the elimination method is about eliminating one of the terms containing any of the variables to make the calculations easier.

This is done by dividing or multiplying a number by the equation(s) such that the coefficients of any one of the variable terms become the same.

Then, we subtract or add both the equations to eliminate or remove that term from the result. The elimination method is called the addition method. For example, solve these two linear equations containing two variables by the elimination method.

Solving the system of linear equations by using the elimination method?

The elimination method is used to solve systems of linear equations of two variables by eliminating a variable and calculating the value of the variable to find the solution. Using the elimination method to solve a system of linear equations with two variables.

 Consider two linear equations

 2x-y=8..>(1)

X+Y=1..>(2)

Solution:

2x-y=8..>(1)

X+Y=1..>(2)

Add equations (1) and (2)

math 3 01

3x=9

X=9/3

X=3

Put the value of x in equation 2

3+y=1

Y=1-3

Y=-2

X=3 and y=-2

Step solve the system of linear equations by using the elimination Method

The elimination method is useful to solve a system of linear equations with two or three variables. We can solve three equations as well using this method. But it can only be applied to two equations at a time. steps to solve a system of linear equations using the elimination method

Step-1: The first step is to divide or multiply both the linear equations with a non-zero number to get a common coefficient of any one of the variables in both equations.

Step-2: subtract or add both the equations such that the same terms will get eliminated.

Step-3: Simplify the result to get a final result of the left out variable (let’s say, y) such that we will only get an answer in the form of y=c, where c is any constant.

Step-4: At last, substitute this value of a variable in any of the given equations to find the value of the other given variable

For example:

Considered two linear equation

x+y=5..>(1)      

2x-3y=5..> (2)

Solution:

x+y=5..>(1)      

2x-3y=5..> (2)

Multiplying 2 by equation (1) on both side

2x+2y=10…>(3)

Subtract equation 2 from 3

math 3 02 1 1


Put the value of y in equation (1)

x+y=5

x+1=5

x=5-1

x=4

x=4 and y=1

Summary

The elimination method is used to solve a system of linear two or three-variable equations.

This method is simple and easy and makes the calculations easier as it eliminates one variable and hence, reduces the calculations.

We make the coefficient of a variable identical to eliminate the corresponding variable

There are various ways of solving linear equations in two variables like the graphical method, the substitution method, the elimination method, and the determinant method. The cross multiplication method.

Systems of Linear Equations: Basics and Methods

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System of linear equations is a collection of two or more linear equations that need to be solved simultaneously. Solving a system of linear equations means finding the values of the unknown variables .

In this article, we will discuss method of solving systems of linear equations.

What is a Linear Equation?

A linear equation has the following format:

ax + by = c

Where a and b are coefficients, x and y are variables, and c is a constant.

For example,

  • 3x + 2y = 12
  • 5x – y = 20

These are linear equations with two variables, x and y.

What is a System of Linear Equations?

A system of linear equations is two or more linear equations working together.

For example,

3x + 2y = 12

5x – y = 20

This is a system of two linear equations with two variables. The goal is to find the values of x and y that satisfy both equations simultaneously.

Systems can have more than two equations and variables, but the concept remains the same.

Methods for Solving Systems of Linear Equations

There are several different methods that can be used to solve systems of linear equations.

  • Graphical method
  • Substitution Method
  • Elimination Method
  • Cross-Multiplication Method
  • Matrix method

1: Graphing

  • Graph each linear equation on the x-y coordinate plane.
  • The point where the graphs intersect is the solution to the system.
  • This method is helpful for visualizing systems of two equations.

2: Substitution

  • Isolate one variable in one of the equations.
  • Substitute the expression for that variable into the other equations.
  • Solve the new equation to find one variable’s value.
  • Substitute this value to find the other variable.

3: Elimination

  • Make coefficients of one variable the same in all equations.
  • Add equations together to eliminate that variable.
  • Solve the new equation to find one variable’s value.
  • Substitute this value to find the other variable.

These are the three main methods used to solve systems of linear equations.

Examples

Examples of solving a system using these three methods.

System:

3x + 2y = 12

5x – y = 20

Graphing

Graph both equations on the x-y plane. The intersection point is at (2, 4). Therefore, x = 2 and y = 4.

Substitution

Isolate y in the first equation:
y = (12 – 3x)/2

Substitute this into the second equation:
5x – (12 – 3x)/2 = 20
9x – 6 = 20
9x = 26
x = 26/9 = 2

Now substitute x = 2 back into the first equation to get y = 4.

Elimination

Multiply the first equation by -5:
-15x – 10y = -60

Add it to the second equation:
-15x – 10y = -60
5x – y = 20
-10y = -40
y = 4

Substitute y = 4 back into an equation to get x = 2.

The same solution is reached through all three methods.

A system of linear equations contains two or more linear equations working together. They can be solved by graphing, substitution, or elimination methods.

Also Read Solving Linear Equations in One Variable

FAQs

Can a system of linear equations have no solution?

Yes, if the equations are inconsistent or contradictory, the system can have no solution. The graphs would be parallel lines that never intersect.

What if a system has infinite solutions?

This occurs when the equations are dependent, meaning one equation can be multiplied to become the other. The graphs would coincide and give infinite points of intersection.

What is a linear equation?

A linear equation is an equation that can be expressed in the form ax + by = c, where a, b, and c are constants, and x and y are variables.

How do you know which method to use to solve a system?

Graphing works well for visualizing two equations. Substitution is helpful if one variable can be easily isolated. Elimination is best if coefficients can be made equal. Trying different methods helps determine the quickest route.

Introduction to Mathematics-History, Branches, And Scope

What is Mathematics?

image of What Is Math

Mathematics is the study of structure, order, and relationships. Over time, the fundamental techniques of counting, measuring, and describing the shape of objects have evolved.

It studies quantity, structure, space, and change. By rigorous deduction from appropriately chosen axioms and definitions, mathematics involves finding patterns, formulating conjectures, and establishing truth.

The entities that are stipulated with certain properties called axioms include arithmetic, geometry, algebra, number theory, formulas, formulas, calculus, proofs, and abstractions from nature.

A mathematical proof consists of a succession of applications of rules that have already been proven, as well as some basic properties that are considered to be the true starting points of the theory.

Mathematics comes from the Greek word “Mathema” which means measure, ratio, and knowledge.

Who is the Father of Mathematics?

Ancient Greek mathematicians introduced mathematics to the world. Several topics from various parts of the world were contributed by mathematicians at the same time. Nobody is credited with inventing mathematics.

Archimedes is famous for being a Greek mathematician who is regarded as the father of mathematics. He is considered the Father of Mathematics for his significant contribution to the development of mathematics.

Notable inventions of Archimedes are His method to find the circumference of the circle by using the method of exhaustion to find the area of the circle and his use of the formula πr2 (the famous pi or pi) to calculate the area of the circle.

image showing the father of mathematics

History of Mathematics

Mathematics has been part of the physical sciences for hundreds of years. Quantitative aspects of the life sciences have been assumed by it.

The history of mathematics deals with the beginnings of mathematical methods and how they were used in the past. The Egyptians did mathematics before the modern age, and the spread of knowledge, in this version. 

The examples of their new mathematical developments were written down in a few places. The importance of citations is very important in mathematics and statistics. The basis for referencing mathematical research can be provided by them. 

When presenting the results of a mathematician’s own publication, it is customary to cite the original work of that mathematician. 

For purposes of taxation, commerce, and trade and also to record time and formulate calendars, the states of Mesopotamia, Akkad, and Assyria, as well as Ancient Egypt and the Levantine state of Ebla, began using arithmetic, algebra, and geometry from 3000 BC.

The history of Mesopotamian and Egyptian mathematics is based on the original documents written by the scribe. Although there are very few documents left in Egypt, these are all of a type and leave no doubt that Egyptian mathematics was, on the whole, elementary and profoundly practical in its orientation. 

Mesopotamian mathematics was much more advanced than Egyptian mathematics. It had a combination of both writing and math, and it had a large number of clay tablets, which showed the mathematical achievements of a much higher order than those of the Egyptians.

The oldest copies of the Greek mathematical documents are in Byzantine manuscripts dating from the 10th century, and from the period before Alexander the Great, no Greek mathematical documents have been preserved except for fragmentary paraphrases. 

This is completely different from the situation described in Egyptian and Babylonian documents.

The invention of printing has solved the problem of obtaining secure texts and has allowed historians of mathematics to concentrate their editorial efforts on the correspondence or the unpublished works of mathematicians.

Historians can only treat the major figures in detail for the period from the 19th century on, because of the exponential growth of mathematics. There is a problem of perspective when the period gets closer to the present.

The birth of mathematics was thought to have occurred among the ancient Greeks until the 1920s. What was known of earlier traditions, such as the Egyptian as represented by the Rhind papyrus (edited for the first time only in 1877).

image showing the top 20 mathematicians

Significance Of Mathematics In Sight Of Scientists

Mathematics has long been recognized as an essential and indispensable field of study. As it has a wide range of applications in diverse fields such as science, engineering, economics, and art. 

Its significance has been acknowledged by numerous prominent scientists throughout history. Here are some views on the importance of mathematics, from Bertrand Russell’s famously skeptical quote to Gauss’s declaration that arithmetic is the queen of all mathematics.

  •  “The subject in which we never know what we are talking about, nor whether what we are saying is true”. (Betrand Russell-1901)
  • “Mathematics is the queen of sciences and Arithmetic is the queen of all mathematics”. (Gauss)
  • “Mathematics is an indispensable instrument of all physical research”. (Kant)
  • “Mathematics is the gateway and key to all sciences”. (Bacon)
  • “Mathematics is the language of physical sciences and certainly, no more marvelous language was created by the mind of man”. (Lindsay)
  • “Mathematics is a way to settle in the mind a habit of reasoning”. (Locke)
  • “Mathematics is engaged, in fact, in the profound study of Art and the expression of beauty”. (j.B.Shaw).

Branches of Mathematics

image of branches of math

Mathematics can be broadly grouped into the following branches:

Arithmetic

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Arithmetic is about adding, subtracting, multiplying, and dividing. For the sake of simplicity, we will denote these operations by the given symbols.

Algebra

The branch of mathematics that helps in the representation of problems or situations in terms of mathematical expressions is called Algebra. Adding, subtracting, multiplication and division are some of the mathematical operations that involve variables, x, y, and Z. 

The use of the branches of mathematics such as trigonometry, calculus, coordinate geometry, and so on is referred to as Algebra. Here’s a very simple example of an equation: (3x) x (2x) = 12

Geometry

Geometry is a branch of mathematics that deals with the shapes and sizes of things.

It also studies how shapes fit together and how things relate to other things.

It is the most practical branch of mathematics. The basic elements of geometry are points, lines, angles, surfaces, and solids.

Trigonometry

The study of angles and their applications to calculations is referred to as trigonometric. It’s also referred to as the geometry of angles. The three basic functions in trigonometry are sine, cosine, and tangent. 

The other three functions that are cotangent, Secant, and Co Secant are derived from those three functions. These functions are the basis for all trigonometric concepts.

Calculus

Calculus is the branch of mathematics that deals with instantaneous rates of change. In the 17th century, two mathematicians, one from England and the other from Germany, created calculus.

Scope of Mathematics

There are lots of options for a career in mathematics. Many fields are related to social sciences, medicine, engineering, and natural science. 

Business problems, scientific problems, and economic problems are some of the things mathematics is used for. Here are some career opportunities a mathematician can pursue in:

  • Professor
  • Statistician
  • Mathematician
  • Data Analyst / Business Analyst
  • Chartered Accountant
  • Investment Banker
  • Data Scientist
  • Astronomer
  • Programmer/ Software Engineer/ Blockchain Developer
  • Economists
  • Engineering
  • Physicist

Studying mathematics can be highly beneficial for our mental development, as it fosters discipline and logical reasoning skills. Moreover, possessing mathematical knowledge is essential for comprehending various other academic subjects, including science, social studies, and even the arts.

By delving into mathematics, we can enjoy a range of advantages that positively impact our minds. These include the cultivation of analytical thinking, the acceleration of mental processes, the enhancement of practical problem-solving skills, and the applicability of mathematical principles to everyday life.

It’s worth noting that mathematics is a ubiquitous presence in our daily routines.

  • Mathematics plays a fundamental role in bringing order to our daily lives. It nurtures essential qualities such as reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability, and effective communication skills in those who study it.
  • By helping us comprehend the world around us, mathematics serves as a powerful tool for cultivating mental discipline.
  • Mathematics teaches you how to approach problems with logic and reason, fostering your problem-solving abilities, creativity, abstract thinking, and communication skills.
  • Mathematical literacy is an essential attribute for leading a successful life. It encompasses fundamental skills such as computational proficiency, quantitative reasoning, spatial ability, and more.
  • In marketing, quantitative analysis is a valuable tool. It enables us to discern patterns, forecast trends, and quantify relationships. Math helps us interpret the world around us and uncover interconnections that exist between things, demonstrating how one element is linked to another.
  • Mathematics is a versatile discipline utilized in numerous fields and industries, including science, engineering, and economics. It plays a critical role in resolving issues and understanding intricate concepts.

Applications Of Math In Different Fields

Mathematics plays an important role in every field of life. Here are some applications of mathematics:

Math In Environmental Science

In environmental science, math plays a crucial role in tasks ranging from counting the number of species in an ecosystem to solving complex chemistry and physics equations related to energy production. 

Environmental science majors take courses in biology, chemistry, geology, and math. Upper-level courses build on this foundation and apply the knowledge to solve current environmental problems by synthesizing and integrating basic sciences.

Math In Medicine

Mathematics is essential in healthcare. It assists in determining the effectiveness of treatments and medication, evaluating disease spread, and prescribing the correct dosage to patients. 

Probability and statistics play a significant role in validating new drugs, while statistical graphs help to illustrate treatment success rates and other significant data points.

Math In Technology

Mathematics technology includes tools like graphing calculators, spreadsheets, and software designed for math. These tools help scientists and engineers organize and structure their knowledge to create systematic, reproducible, and transmittable knowledge.

Math In Nature

Mathematics plays a significant role in genetics and evolution, enabling us to comprehend the changes and variations in population size and physical characteristics through mathematical models. 

Nature presents numerous examples of mathematical concepts, such as symmetry, which is observed in the six-fold radial symmetry of a snowflake.

Math In Daily Life

Mathematics is the universal language that helps us understand patterns, define relationships, and predict the future.

Banking and financial services rely on math for accuracy in managing money and calculating bills and financial obligations.

Cell phone technology requires basic math skills for phone operations and functions.

Computer science relies heavily on mathematics for data entry, computer operation, and software development.

Technological innovation, such as the Internet, is developed with the help of mathematics.

 Math is widely used in animation design, architecture, sports, population geography, astronomy, music, painting, fashion designing, home decoration, and in the kitchen.

Topic Wise Mathematics Articles

Basics of Mathematics

What is Decimals Mean in Math?

Brackets in Math | Types of Brackets

Ascending Order Mean in Math | Difference Between Ascending And Descending Order

What is Descending Order Mean in Math?

What is Division Mean in Math?-Division Algorithm

Square Root Mean in Math-Definition, Symbol, Formula

What is Quotient Mean in Math?-A different Form of Quotient

What is Odd Number Mean in Math?-Definition, And Properties

What is Even Number Mean in Math?-Definition, Properties

What is Divisor Mean in Math?-Definition, And Formula

What is a Remainder Mean In Math?

What is Numerator Mean in Math?

What is an Exponent Mean in Math?

What does undefined mean in math?

What Does Sigma (σ) Mean in Different Fields?

What Does Product Mean in Math?

Finding a Percentage of a Whole Number? | What is the Percentage?

How can i help my child improve in math?

Does Playing Chess Improve Your Math Skills?

How can i improve my math grades? Expert Opinion

Math Improvement Tips That Work Wonders

Important mathematical Symbols with name, meaning, and examples

How mathematics is used in different fields?

Why math is difficult for students? A detailed analysis

Length Mean in Math

Infinity Mean in Math

What is Cub Root Mean in Math?

What is the Cube Number?-Definition, Cube of Fraction, And Negative Number

What is Composite Number Mean in Math?

What is Denominator Mean In Math?

What Does the Symbol Mean in Math?

Difference Between In Math

Ascending Order Mean in Math | Difference Between Ascending And Descending Order

Difference Between Proper And Improper Fraction

Types of Subset | Difference Between a Proper And Improper Subset

Difference Between a Finite Set And an Infinite Set

Difference between Set and Subset

Difference between Permutation and Combination

Difference between Linear and Nonlinear Equation

Difference between Natural numbers and Whole Numbers

Difference between Variables and Constants

Difference between Rational and Irrational Numbers

Difference Between Sequence and Series

Difference Between Fractions and Rational Numbers

Difference between Rows and Columns

Algebra

Collinear Points-Definition, Formula, And Methods To Find Collinear Points

Substitution Method Mean in Math?
Elimination Method Mean in Math?
What Does Coefficient Mean in Math?
What Does Expression Mean in Math
Series and Sequences

Sequence-Finite Sequence and Infinite Sequence

What is a Sequence in Math

What Is Arithmetic Progression? | Sequence

What is Series in Math?

Harmonic Progression | Sequence In Math

Partial Fractions

Difference Between Proper And Improper Fraction

Mixed Fraction Mean in Math

What is a Like Fraction Mean in Math?

What is a Unit Fraction Mean In Math?

How to Find Equivalent Fractions?

Types of Fraction Mean in Math

Equivalent Fraction Mean in Math

What is a Fraction Mean in Math?-Representing a Fraction

What is Ratio in Math?-EDUInput

The Four Cases of Partial Fractions Resolutio

Basics Statistics

Arithmetic Operation Mean in Math?

What Does Mode Mean in Math?

What is the Geometric Mean?

What is Arithmetic Mean in Math?

Calculators

Inches to Centimeters Converter

Mastering Yard to Feet Conversion

Percentage Difference Calculator

Meter To Kilometer Calculator

Square Meter To Square Feet Calculator

Feet to Centimeter Calculator

Centimeter To Millimeter Calculator

Meters To Centimeters Calculator

Millimeters to Centimeters Calculator

Gallon To Liter Calculator

Kilometer to Mile Calculator

Feet to Centimeter Calculator

lbs to kg Converter Calculator

Meter To Feet Calculator

Differentiation

What is a Variable Mean in Math?-Types of variables in math

Derivative of a Product Rule-Product Rule Formula

How to Apply the Product Rule of Differentiation?

Factorization

How to Find Prime Factorization by Division Method?

What is Prime Factorization Mean in Math?

How to Find Square Roots of a Number by Prime Factorization?

What Does Factor Mean in Math?

Functions and Limits

Types of Polynomial On the Basis of Number of Terms

Polynomial Mean In Math-Definition, Degree, And Notation

What Does Range Mean in Math?

Y-Intercept in Mathematics

Fundamentals of Trigonometry

Quadrant Mean in Math

Complete Angle-Definition, Representation, And Formation

Reflex Angle-Real-life Example of Reflex Angle

Straight Angle-Properties of Straight Angles

Obtuse Angle-Obtuse Angle Triangle

What Is the Right Angle?-Definition, Example, And Triangle With Right Angle

Acute Angle-Definition, Properties, And Formula

What is Angle?–Definition-Types of Angle

What Does Perpendicular Mean in Math?

Fundamentals of Trigonometry | Angle, Vertex of angle, Radian, Circular system

Trigonometry Formulas | Sign of Trigonometric Functions in Different Quadrants

Units of Measures of Angles in Math

Group

What is DeMoivre’s Theorem?

Cyclic Group – Theorem of Cyclic Group

Theorems of the Subgroup

SubGroup -Types and Examples

HCF & LCM

How to Find LCM by using the Division Method?

How to Find HCF by Division Method of Two Numbers?

How to Find HCF by Listing Factor Method?

How to Find HCF by Prime Factorization Method?

Highest Common Factor (HCF) Mean in Math

How to Find LCM By Using Prime Factorization Method?

How to Find LCM BY Using the Listing Method?

Least Common Multiple(LCM) Mean in Math

Linear inequalities and Linear Programming

Linear Inequality Mean in Math

Rules of Linear Inequality-Addition, Subtraction, And, Multiplication

What is a Linear Equation-Definition-Standard form- Example

Sequence-Finite Sequence and Infinite Sequence 

Logaritham

Scientific Notation Mean in Math-Scientific Notation Rules

What is a Symbol of logarithm? | What is a Symbol of Exponential?

Matrices and Determinants

What is an Orthogonal Matrix?-Example of Orthogonal Matrix

Operations On Matrix | Transpose of a Matrix and Inverse of Matrix

What are Matrices and Determinants | Types of Matrices

Number System

What is a Number?-Definition, Examples, and History

Number System-Definition, Types, And Examples

Types of Decimals | Properties of Decimals

What are the Major Properties of Integers?

Integers Operation-Definition, And Rules of Integers

Integers Numbers-Definition, Symbols, And Types

What are the Properties of Whole Numbers?

What is a Prime Number Mean in Math?

Whole Numbers Mean in Math-Definition, And Representation

Natural Number Mean in Math?

What is Integer Number?

Basic Properties of Real Number-Distributive, Closure, Associative, And Commutative

What is a Real Number?-Definition, And Symbol

Geometrical Representation of Complex Numbers

Complex Number-Operations on Complex Number

Rational Numbers and Irrational Numbers – Definition and Example

Properties of Real Numbers

Operation on Set

What is Subset Mean in Math? | How to Find the Number of a Subset of a Set

Types of Subset | Difference Between a Proper And Improper Subset

Empty Set Mean in Math | How to Denote an Empty Set

What is a Power Set Mean in Math?-Definition, And Properties

Permutation Combination and Probability

Factorial Mean in Math

Frequency Distribution | Construction of Frequency table

Probability-Addition of Probabilities and Multiplication of Probabilities

Permutation and Combination – Definition, Formulae, and Examples

What is Combination in Math Formula with Example

Circular Permutation in Math

Probability Mean in Math|Types of Probability

What is Factorial Mean in Math

Quadratic Equation

Degree of Polynomial Function-Classification of Degree of a Polynomial

Roots of a Quadratic Equation | Discriminate of Quadratic Equation

Relations between the Roots and the Coefficients of a Quadratic Equation.

Polynomial Function | Remainder Theorem, Factor Theorem, and Synthetic Division

Equations Reducible to the Quadratic Equation-Types with example

Four Fourth Roots Of Unity

Three Cube Roots Of Unity

Introduction to Quadratic equation

Set Function & Group

Set Builder Notation Mean in Math | Rule For Set Builder Notation

Difference Between a Finite Set And an Infinite Set

Roster Form of a Set-Definition, Venn Diagram, And Limitation

What is Universal Set Mean in Math?

Functions-Types of Function

What is Group and Abelian Group?

Binary Operations | Properties of Binary Operation

Inductive and Deductive Logic

Properties of sets

Introduction to operation of set-Edu input

What is Set in mathematics? Explained with examples

Variations

Types of Proportions –Properties of Proportional

What is a Proportional Mean in Math?

What Does Reciprocal Mean in math?

Vectors

Addition of Two Vectors Mean in Math

Geometric Interpretation of Vector

What is a Vector Mean in Math

Examples in Math

10 Examples of Acute Angles in Math

10 Examples of Additive Inverses in Math

Examples of Algebra in Real Life

10 Examples of Algorithms in Math

10 Examples of Arithmetic Sequences in Math

10 Examples of Angles in Math

Examples of Area in Math

3 Examples of Asymptotes

10 Examples of Binomial Distribution in Mathematics

10 Examples of Calculus

10 Examples of Cardinal Numbers

10 Examples of Circles in Math

10 Examples of Coefficients in Math

10 Examples of Combinations in Math

10 Examples of Complementary Angles

10 Examples of Composite Numbers

10 Examples of Compound Interest

10 Examples of Congruent Figures in Mathematics

10 Examples of Constants of Proportionality

10 Examples of Cubes in Mathematics

10 Examples of Deductive Reasoning in Math

10 Examples of Derivatives

10 Examples of Diameter

10 Examples of the Distributive Property

10 Examples of Differential Equations

10 Examples of Direct Variation

10 Examples of the Distance Formula

10 Examples of Divisors in Mathematics

8 Examples of Exponential Decay in Mathematics

10 Examples of Exponential Growth

10 Examples of Exponents in Mathematics

10 Examples of Factoring

10 Examples of Functions

8 Examples of Geometric Sequences

10 Examples of Graphs

10 Examples of Integers

10 Examples of Intersecting Lines

10 Examples of Inverse Variation

10 Examples of Mean

10 Examples of Median

10 Examples of Natural Numbers

10 Examples of Mode

20 Examples of Parallel Lines

20 Examples of Perpendicular Lines in Real Life

10 Examples of Polygons

10 Examples of Polynomial Functions

10 Examples of Probability

10 Examples of Pyramids

10 Examples of Pythagorean Theorem

10 Examples of Quotients

10 Examples of Ratios

20 Examples of Rational Numbers

10 Examples of Real Numbers

10 Examples of Sample Spaces

10 Examples of Scientific Notation

10 Examples of Simple Interest

10 Examples of Slope

20 Examples of Square Root

10 Examples of Standard Deviation

10 Examples of Subsets

10 Examples of Supplementary Angles

10 Examples of Triangles in Real Life

10 Examples of Vectors

10 Examples of Venn Diagrams in Math

10 Examples of Vertical Angles

10 Examples of Volume in Mathematics

10 Examples of Y-Intercept

10 Examples of Variables

10 Examples of Systems of Equations

10 Examples of Surds in Mathematics

10 Examples of Rate of Change

10 Examples of Approximation

10 Examples of Altitude

5 Examples of Arc Length

10 Examples of Axis of Symmetry

10 Examples of Bisectors

10 Examples of the Cartesian Plane

10 Examples of Central Tendency

10 Examples of Circumference

7 Examples of Absolute Value

Related FAQs

What is the definition of math?

The study of mathematics involves the application of logic and reasoning to abstract concepts and models. Mathematics is the art of problem-solving. Mathematics is the science of patterns and relationships

What is math and its uses?

Mathematics is the science of logical shape, quantity, and arrangement. It is everywhere in our lives, from mobile devices and computers to software and architecture (both ancient and modern). Math even underpins art, money, engineering, and sports.

Who is the father of maths?

The Father of Math is the one and only Archimedes – a great Greek mathematician and philosopher.

What is math example?

The definition of mathematics is the branch of science that deals with the study of numbers, shapes, and their relationships. An example of mathematics is arithmetic, the study of addition, subtraction, multiplication, and division.

How many types of math are there?

There are different types of mathematics

  • Algebra
  • Geometry
  • Trigonometry
  • Arithmetic

What is mathematics in the modern world subject?

Mathematics in the Modern World is a course designed to give students a better understanding of the field of mathematics and how it’s being used in the real world.

In the modern world, Mathematics is not just a boring subject you have to take to graduate high school. It can be a lot of fun, especially when it comes to writing copy that gets people excited! While you don’t necessarily have to hire a professional copywriter to do this for you, learning the best practices will give anyone an advantage over competitors!

Why is math good for your brain?

There are many benefits to studying mathematics, including enhancing analytical and problem-solving skills, fostering systematic and logical thinking, and broadening the mind to handle unfamiliar tasks with confidence.

Substitution Method Mean in Math?

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One of the methods to solve a system of linear equations in two unknown variables algebraically is the substitution method. In this method, we find the value of any one of the unknown variables by isolating it on one side and taking every other term on the other side of the equation.

Then we substitute that value in the second equation. It includes simple steps to find the values of variables of a system of linear equations by the substitution method. Let’s this article learn about it in detail.

What is the substitution method?

The substitution method is a simple method to solve a system of linear equations algebraically and find the solutions to the unknown variables.

 As the name offer, it includes finding the value of the x-variable in terms of the y-variable from the first equation and then substituting or putting the value of the x-variable in the second equation.

In this method, we can solve and find the value of the y-variable. And at last, we can put the value of variable y in any of the given equations to find the value of variable x this method can be interchanged as well where we first solve for x and then solve for.

Definition of substitution method

The substitution method is one of the algebraic way to solve a system of linear equations. It includes substituting the value of any one of the unknown variables from one equation to another equation.

 The other two algebraic methods of solving linear equations are the cross multiplication method and the elimination method. Apart from the algebraic process, we can also solve a system of linear equations graphically.

For example: solving two linear equations x+2y=7and x+y=1

 Using a substitution method.

Solution:

Substitution Method

x+2y=7…>(1)

x+y=1…>(2)

From equation (2)

X=1-y

Substitute this value equation (1)

1-y+2y=7

Y=7-1

Y=6

Substitute this value equation (2)

X+6=1

X=1-6

X=-5

X=-5 and y=6

Solving the system of linear equations by substituting the method

The steps to the substitution method or application to solve a system of linear equations are given below:

Step 1: Simplify the given linear equation for two variables by expanding the parenthesis if needed.

Step 2: Solve any one of the linear equations for any one of the variables. You can use any unknown variable based on the ease of calculation.

Step 3: Substitute the obtained value of x or y to solve any one of the linear equations in the other linear equation.

Step 4: Now, the new equation is obtained using arithmetic operations and solving the equation for one variable.

Step 5: Now, substitute the value of the unknown variable from Step 4 in any of the given equations to solve for the other variable.

For example:

3X+2Y=8…>(1)

X+y=4..>(2)

From equation 2

X=4-y

Substitute this value equation (1)

3(4-y)+2y=8

12-3y+2y=8

-y=8-12

-y=-4

Y=4

Substitute this value equation (2)

X+4=4

X=4-4

X=0

X=0 and y=4

What is a Linear Equation-Definition-Standard form- Example

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A linear equation is an equation in which the greatest exponent of the variable is always one (1). It is also called a one-degree equation. The general form of a linear equation in one variable is of the form ax + b = 0.

Here, x is a variable, a is a coefficient of variable x and b is constant. The general form of a linear equation in two variables is of the form ax + by = c. Here, x and y are variables, a is a coefficient of variable x and b is a coefficient of variable y and c is a constant.

What is a linear equation?

A linear equation is an equation in which the highest exponent of the variable is always one (1). It is also known as a one-degree equation. The linear equation graph is a straight line.

The standard form of the linear equation of one variable.

ax + b = 0

x is a variable

a is a coefficient of the variable

 b is constant

The standard form of a linear equation in two variables

 ax + by = c

, x and y are variables

, a is a coefficient of variable x  

b is a coefficient of variables y

 c is a constant.

Where a, b, and c are any real numbers, and x and y are the variables

For example:

EquationLinear or non-linear equation
5x+3=0linear
y = x2 – 7Non-linear, the exponent of the variable x is 2
2x+3y=5linear
y2 – x = 9Non-linear
2x+9=0linear

Linear equation in a standard form

The general form or standard form of linear equations in one variable is written as, ax + b= 0; where a and b are real numbers, and x is the single variable. The general form of linear equations in two variables is expressed as, ax + by = c; where a, b, and c are any real numbers, and x and y are the variables.

MATH 2 01

What is a linear equation in one variable?

A linear equation in one variable is an equation in which there is only one variable included or present. It is a general form of the linear equation one variable, ax + b= 0, where x is an unknown variable and a and b are any two real numbers that have only one solution.

This equation has a degree that is always equal to one. Can be solved a linear equation in one variable very easily. The variables are separated and brought to the left-hand side of the equation and the constants are brought and combined to the other side (right–hand side) of the equation, to get the value of the variable.

For example:

Solve the linear equation in one variable 2x-4=8

Solution:

2X-4=8

2X=8+4

2X=12

X=12/2

X=6

What is a linear equation in two variables?

A linear equation in two variables is of the form ax + by =c, in which x and y are the two variables, and a, b, c are real numbers and each with a degree of 1.

 For example,

5x + 3y + 9 = 0 is called a linear equation in 2(two) variables. There are different ways of solving linear equations in two variables like the graphical method, the cross multiplication method the substitution method, the determinant method and the elimination method.

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