How to Solve Simultaneous Equations Graphically

There are several ways to solve for a linear system of simultaneous equations and the ones that we've explored already are the method of substitution and the method of elimination.

Another method, and it's my favourite method, is to solve simultaneous equations graphically.


I've got a system of 2 linear simultaneous equations here:

1. y = 3x - 3
2. ½x - y = -2

Now to graph these equations, I need them to be in the form of y = mx + c, where m is the gradient and c is the y-intercept. And it looks like in equation (1), we've already got the equation in that form.

With equation (2), we can rearrange it to become...

y = ½x + 2

Then we can graph these 2 equations on the Cartesian plane. The point where they cross each other is the solution to this system of simultaneous equations.

In this case, the lines cross each other at the point (2,3), which means the solution to this problem is

x = 2

y = 3