Question

Which represents the solution(s) of the system of equations, y = x2 – 2x – 15 and y = 8x – 40? Determine the solution set algebraically.

(–5, –80)
(5, 0)
(5, 0) and (–5, –80)
no solutions

Answer 1

Answer: b

(5,0)

Explanation:

Answer 2

(5, 0 )

Explanation:

Given the 2 equations

y = x² - 2x - 15 → (1)

y = 8x - 40 → (2)

Substitute y = x² - 2x - 15 into (2)

x² - 2x - 15 = 8x - 40 ( subtract 8x - 40 from both sides )

x² - 10x + 25 = 0 ← in standard form

(x - 5)² = 0 ← in factored form, thus

x - 5 = 0 ⇒ x = 5

Substitute x = 5 into (2) for corresponding value of y

y = 8(5) - 40 = 40 - 40 = 0

Solution is (5, 0 )