# How to Solve Simultaneous Equations Using a Graph

## Solving Simultaneous Equations Using a Graph

Simultaneous equations are a set of several equations with several unknowns.

We can use a graph to find the values of the unknowns which solve both equations at the same time.

If both equations are plotted as a line on a graph, the solution is where the lines cross. • The value of x that solves the simultaneous equations is given by the x-coordinate of the point where the lines cross.

• The value of y that solves the simultaneous equations is given by the y-coordinate of the point where the lines cross.

## How to Solve Simultaneous Equations Using a Graph

Solving simultaneous equations using a graph is easy.

### Question

Solve the simultaneous equations shown below using a graph. # 1

Plot Equation (1) on a pair of axes. ### How to Plot a Linear Equation as a Line

Here is a quick way to draw a linear equation as a line:

• Find where the line crosses the y-axis by substituting x = 0 into the equation.

( 0 ) + y = 5 ∴ y = 5 • Find where the line crosses the x-axis by substituting y = 0 into the equation.

x + ( 0 ) = 5 ∴ x = 5 • Join the two points with a line. # 2

Plot Equation (2) on a pair of axes. # 3

Find where the lines cross. # 4

Read off the x-coordinate of this point. x = 3 solves the simultaneous equations.

# 5

Read off the y-coordinate of this point. y = 2 solves the simultaneous equations.

We have solved the simultaneous equations:

x = 3, y = 2 solves

x + y = 5
x − y = 1

## Slider

The slider below shows another real example of how to solve simultaneous equations using a graph.

Open the slider in a new tab