Q:

Solve the system of equations y=x^2-2 y=-2x+1

Accepted Solution

A:
Answer:DStep-by-step explanation:Given the 2 equationsy = xΒ² - 2 β†’ (1)y = - 2x + 1 β†’ (2)Substitute y = xΒ² - 2 into (2)xΒ² - 2 = - 2x + 1 ( subtract - 2x + 1 from both sides )xΒ² + 2x - 3 = 0 ← in standard form(x + 3)(x - 1) = 0 ← in factored formEquate each factor to zero and solve for xx + 3 = 0 β‡’ x = - 3x - 1 = 0 β‡’ x = 1Substitute these values into (2) for corresponding values of yx = - 3 : y = -2(- 3) + 1 = 6 + 1 = 7 β‡’ (- 3, 7 )x = 1 : y = - 2(1) + 1 = - 2 + 1 = - 1 β‡’ (1, - 1 )