Solve the simultaneous equations: y=2x+2, y=x^2 - 1

The solution to this question can be obtained algebraically using substitution. As both equations are equal to y, this also means they are equal to each other. So firstly, substitute the simpler equation which is y=2x+2 into the second equation giving 2x+2 = x^2 - 1. Re-arrangement of this gives x^2 - 2x + 3 = 0. Using quadratic equation theory, this then becomes (x - 3)(x + 1)=0. Any equation that equals zero must have another zero value on the other side of the equation. Therefore when y is 0, x is either 3 or -1. Using these two x values, we can work out the y values from the original equations. Using the simpler equation y=2x + 2, if x is 3 then y=2*3 + 2= 6+2 = 8 and if x is -1, y=2(times-1) + 2 = -2+2=0. Just to check these values are correct, you can then plug them in to the second equation and the same x and y values should be obtained