Question

he first three steps in determining the solution set of the system of equations, y = –x2 – 2x + 8 and y = 2x + 11, algebraically are shown in the table. Which represents the solution(s) of this system of equations?

Answer 1

Question:

Which represents the solution(s) of this system of equations?

Answer:

(-3,-1)

Answer 2

The solutions are -3 and -1

Explanation:

∵ y = -x² - 2x + 8

∵ y = 2x + 11

∴ -x² - 2x + 8 = 2x + 11

∴ -x² - 2x - 2x + 8 - 11 = 0

∴ -x² - 4x - 3 = 0 ⇒ divide both sides by -1

∴ x² + 4x + 3 = 0

∴ (x + 3)(x + 1) = 0

∴ x + 3 = 0 ⇒ x = -3

∴ x + 1 = 0 ⇒ x = -1

∴ The solutions are -3 and -1