Solve the system:  y = x2 – 7,  y =  x - 7

To solve the system of equations y = x^2 - 7 and y = x - 7, you need to set the two equations equal to each other and solve for x. Here are the steps:

1. Set the two equations equal to each other:

   x^2 - 7 = x - 7

2. Rearrange the equation to one side:

   x^2 - x = 0

3. Factor the equation:

   x(x - 1) = 0

4. Set each factor equal to zero and solve for x:

   x = 0 or x - 1 = 0, so x = 0 or x = 1

5. Substitute x = 0 and x = 1 into either of the original equations to find the corresponding y values. If we substitute into y = x^2 - 7:

   For x = 0: y = (0)^2 - 7 = -7 For x = 1: y = (1)^2 - 7 = -6

So, the solutions to the system of equations are (0, -7) and (1, -6).