solve the simultaneous equation x^2 + 2y = 9 , y - x = 3

First we need to find a value for x in terms of y , this can be done by rearranging the second equation y - x = 3 to give x = y - 3. This equation is then substituted into the first equation so that everything is in terms of y giving us (y - 3)^2 + 2y = 9. We then multiply out the brackets to give us y^2 - 6y + 9 + 2y = 9 this simplifies to y^2 - 4y = 0. Therefore y = 0 to find the x value we sub this value of y into the second equation to give 0 - x = 3 and solve to find x = -3