Math help...linear and quadratic systems?

y = -2x + 1

y = -2x^2 + 1

Set the y's equal

-2x^2 + 1 = - 2x + 1           subtract 1 from both sides

-2x^2 = - 2x             multiply both sides by -1

2x^2 = 2x       divide both sides by 2

x^2 = x     subtract x from both sides

x^2 - x = 0       factor

x ( x - 1) = 0

Setting each factor to 0  and solving for x produces two  solutions at

x = 0      and   x =  1