Solve the simultaneous equations 2x+2y=14 and 3x-y=1

To solve these eliminations, we must eliminate either the x's or the y's. Either is possible but let us start with the y's. There is 2y in the first equation and (-1)y in the second, so we will have to multiply the second equation by 2 to ensure we have 2 and -2 lots of y in both equations. This means the second equation becomes 6x-2y=2. We can now add the two equations together to give us 8x=16. Dividing this by 8 gives us x=2. To find y, we pick either of the original equations (let's pick the first one) and substitute x=2 into to give us 4+2y=14. Subtracting 4 from both sides gives us 2y=10 and dividing by 2 finally gives us the solution y=5 (and x=2).