The Lesson

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.

Step-by-Step:

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.

Answer:

We have solved the simultaneous equations:

x = 3, y = 2 solves

x + y = 5

x − y = 1

Lesson Slides

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