Solving simultaneous equations graphically

Simultaneous equations can be solved algebraically or graphically. Knowledge of plotting linear equations is needed to solve equations graphically.

To find solutions from graphs, look for the point where the two graphs cross one another. This is the solution point. For example, the solution for the graphs y = x + 1 and x + y = 3 is the coordinate point (1, 2).

Graph showing plots of y=x+1 & x+y=3

The solution to these equations is x = 1 and y = 2.

Example

Solve the simultaneous equations x + y = 5 and y = x + 1 using graphs.

To solve this question, first construct a set of axes, making sure there is enough room to plot the two graphs.

Graph axes from -10 to 10

Now draw the graphs for x + y = 5 and y = x + 1.

To draw these graphs, use a table of values:

y = x + 1

x-10123
y01234

x + y = 5

x-10123
y65432

Plot these graphs onto the axes and label each graph.

Graph showing plots of y=x+1 & x+y=5

The point of intersection is (2, 3) which means x = 2 and y = 3.