Solve the following simultaneous equations: x^2 + 2y = 9, y = x + 3

When solving simultaneous equations, there are two methods: substitution and elimination. For this question, as one of the equations is a quadratic, the substitution method has to be used. The second equation (y = x + 3) can be used to replace y in the first equation (x^2 + 2y = 9) with x + 3: x^2 + 2(x + 3) = 9 Then we expand the brackets:x^2 + 2x + 6 = 9 Then we subtract 9 from both sides:x^2 + 2x -3 = 0We then factorise this quadratic to get two solutions for x:(x + 3)(x - 1) = 0 x = -3, x = 1Finally, we put the x values back into the equation to get our y values:when x = -3, y= -3 + 3 = 0when x = 1, y = 1 + 3 = 4