Question

Solve the system of equations:
y = 2x - 3
y = x2 - 2x - 8

Answer 1

the solutions to the equations is (-1, -5) and (5, 7)

Answer 2

Explanation:

y = 2x - 3 --------------(i)

y = x² - 2x - 8 -----------(ii)

Substitute y = x² - 2x - 8 in equation (i)

x² - 2x - 8 = 2x - 3

x² - 2x - 8 - 2x + 3 = 0

x² - 2x -2x - 8 + 3 = 0

x² - 4x - 5 = 0

x² + 1x - 5x -5 = 0

x(x + 1) - 5(x + 1) = 0

(x + 1)(x - 5) = 0

x + 1 =0 ; x -5 = 0

x = -1 ; x = 5

When x = -1; y =2*(-1) - 3 = -2 -3 = -5

When x = 5; y = 2*5 - 3 = 10-3 = 7