Solve the simultaneous equations : x ^2+2y=9, y=x+3 to find solutions for x and y.

We must use the substitution method for this question because the first equation is a quadratic. Take the more simple equation (the second one), and use that to substitute the value for y in to the first equation:x^2+2(x+3)=9. Expand the brackets and rearrange to get: x^2+2x-3=0.Now we must factorise, which will give us 2 solutions for x. Factorising gives: (x+3)(x-1)=0.The solutions for x are therefore, x = -3, x = 1. Using these solutions for x and substituting them on to the other equation will give us corresponding solutions for y:When x = -3, y = 0 and when x = 1, y = 4.