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

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:

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

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.

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.