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 xcoordinate of the point where the lines cross.

The value of y that solves the simultaneous equations is given by the ycoordinate 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.
StepbyStep:
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:
2
Plot Equation (2) on a pair of axes.
3
Find where the lines cross.
4
Read off the xcoordinate of this point.
x = 3 solves the simultaneous equations.
5
Read off the ycoordinate 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