Solve the simultaneous equations: 2x+2y=12 x-y=8 You must show your working

The first thing we want to do is change the first equation so it's either all x's or all y's, we don't want a mixture. Now looking at the bottom equation, we can rearrange it by adding y to both sides. This gives us x=8+y. It's important to remember these are simultaneous equations, that means we can substitute in (8+y) whenever it says x in the top equation.

Therefore the top equation is now 2(8+y)+2y=12 Let's expand out the brackets! 16+2y+2y=12 16+4y=12 4y=-4 y=-1

Now to work out x, we'll substitute -1 in whenever we see y in the bottom equation (the top would take longer to work out) x-(-1)=8 x+1=8 x=7