Solve the simultaneous equations: x+y =2; x^2 + 2y = 12

The first thing to note about this question is that it's a simultaneous equations question, involving a quadratic. We will have to use substution in order to solve it. So first of all we need to chose which variable x or y we should work with. There isn't an incorrect choice here as either will lead you to the right answer, but if we choose to work with y intially it makes the calculations easier.
So take our first equation x+y =2, and subtract x from both sides, like this: y = 2-x, now from here we take that expression for y and subsitute it into our second equation. So out second equation: x^2 + 2y = 12, becomes: x^2 + 2(2-x) = 12, expanding out the brackets we get: x^2 -2x +4 = 12, and take away 12 from both sides which will give us: x^2 - 2 - 8 = 0. From here all there is left of the question is to solve this quadratic. Tis quadratic nicely factors into (x-4)(x+2)=0, giving two possible 'x's: x_1 = 4, and x_2 = -2. Now we have 2 'x's all we need is the 2'y's, but this is easy as we simply sub x_1 and x_2 into our first equation: y = 2-x giving us y_1 = 2-4 = -2, and y_2 =2 - (-2) = 4