How do you solve the simultaneous equations 3x+y=5 and x-y=3?

The aim of this question is to find x and y by combining these two equations. There are two ways of solving simultaneous equations, elimination and substitution. Elimination can only be used when there are no non-linear terms, substitution can always be used but is less straightforward. (Check they know what non-linear means, if not:) Non-linear means terms with powers of x or y or xy terms etc. In this question we can use elimination as all the terms are linear. We can eliminate x or y, but y is probably easier. If we add the equations together, the y terms cancel out and we are left with 4x=8, from which we can see that x=2. We then substitute x=2 into one of the equations to find y. If we use the second one, we get 2-y=3, then y=-1. We can check this by making sure the first equation equals 5.