Determine the solution set to the system of equations below algebraically.

Question

y-x^2=2x

4y=8x+4

Answer 1

y-x²=2x

4y=8x+4 (divide by 4), y=2x+1 (plug this into the top equation for y)

2x+1-x²=2x (simplify), x²-1=0, (factor), (x+1)(x-1)=0, x=-1,1 (plug both of these numbers into the y= equation)

y=2(1)+1=3, y=2(-1)+1=-1,

The solutions set is (-1,-1) and (1,3)