Question

Help solve the system of equations

Answer 1

2x + 4 = x^2 + x - 2
x^2 + x - 2 - 4 - 2x = 0
x^2 - x - 6 = 0
(x - 3)(x + 2) = 0

x - 3 = 0          y = 2x + 4
x = 3               y = 2(3) + 4
                       y = 10

x + 2 = 0          y = 2x + 4
x = -2               y = 2(-2) + 4
                        y = 0

solutions are : (3,10) and (-2,0) <===

Answer 2

Given,

y = 2x + 4

Also given,

y = x² + x - 2

Substituting the value of y from above,

2x + 4 = x² + x - 2

x² - x - 6 = 0

x² - 3x + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

(x + 2)(x - 3) = 0

x = -2 or 3


When x = -2,

y = 2x + 4 = (2 * -2) + 4 = -4 + 4 = 0

When x = 3,

y = 2x + 4 = (2 * 3) + 4 = 6 + 4 = 10

Hence, the two solutions are (-2, 0) and (3, 10).

Hence, the answer is C.