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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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