10 Examples of Systems of Equations
In mathematics, system of equations is a collection of two or more equations that share the same set of variables.
In this article, we will discuss ten examples of systems of equations in mathematics.
- Examples of Systems of Equations
Examples of Systems of Equations
These are 10 examples of system of equations.
1: Linear Equations in Two Variables
Classic example of a system of equations involves two linear equations in two variables.
2x + 3y = 7
4x – y = 6
2: Three Equations with Three Unknowns
Systems can have more equations and variables. A system with three equations in three variables is,
x + y – z = 5
2x – 3y + z = 1
3x + y + 2z = 8
3: Distance, Rate, and Time Problems
Systems of equations are useful for solving distance, rate, and time problems.
For example, If you travel 300 miles at a certain speed, it takes 5 hours. If you increase your speed by 10 mph, you can cover the same distance in 4 hours. Find the original speed.
4: Mixing Problems
Mixing problems involve combining solutions with different concentrations. A system of equations help determine the quantities of each solution.
5: Investment and Interest Problems
When calculating investments with different interest rates, a system of equations help determine the amount to invest at each rate to achieve a specific total return.
6: Physics Problems
Physics often involves systems of equations.
For example, equations related to velocity, acceleration, and time are used to solve problems involving motion.
7: Chemical Reactions
Balancing chemical equations is a classic application of systems of equations in chemistry.
8: Economics and Market Equilibrium
Systems of equations are used to model supply and demand in economics, helping to find equilibrium prices and quantities.
9: Circuit Analysis
Electrical circuits are analyzed using systems of equations. The Kirchhoff’s circuit laws are expressed through a system of equations.
10: Optimization Problems
In optimization, we seek to maximize or minimize a particular quantity. Systems of equations are used to formulate constraints and objectives in these problems.