Question

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

Answer 1

Answer: The solution to the system of equations y = x² - 2x - 15 and y = 8x - 40 is (5,0).

Explanation: Substitute y = 8x - 40 in y = x² - 2x - 15

8x - 40 = x² - 2x - 15

Identify the like terms

x² - 2x - 8x - 15 + 40 = 0

Evaluate the equation

x² - 10x  + 25 = 0

Factorize the equation

(x - 5)(x - 5) = 0

Solve for x

x - 5 = 0 and x - 5 = 0

Solving for x gives

x = 5

Substitute x = 5 in y = 8x - 40

y = 8(5) - 40

y = 0