GCSE Style Question and Answer 2

Solve the following pair of simultaneous equations.

1x+2y=3 and 3x+2y=1

This is a question I have made up, where the coefficients are mirrored, 1, 2, 3, 3, 2, 1. This is simple to solve because of the 2y term in both equations. It means that we can subtract the bottom equation from the top one and eliminate the y terms.

As you can see, we have only the x terms remaining, because the 2y terms cancel out after subtraction, therefore it is a simple matter of solving for x.

Once you have a value for x, just substitute it into 1x+2y=3 to find y.