Determine the points of intersection of the line y = -2x + 7 and the parabola y = 2x^2 + 3x - 5.
you want the y of one equation to be equal to the y of the other, so
2x^2 + 3x - 5 = -2x + 7
2x^2 + 5x - 12 = 0
(2x - 3)(x + 4) = 0
x = 3/2 or x = -4
if x = 3/2, y = -2(3/2) + 7 = 4
if x = -4 , y = 8+7 = 15
state the conclusion