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10 Examples of Systems of Equations

October 16, 2023
written by Rida Mirza

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

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.

For example,

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.

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