Algebra homework

Question

How many solutions does the following system have?

y=8x-6

y=2x^2-16x+36

A. Two solutions

B. One solution

C. No solution

D. Infinite solutions

Answer 1

Set the 2 equations = to each other.

2x² - 16x + 36 = 8x - 6

2x² - 24x + 42 = 0

x² - 12x + 21 = 0

Solve using the quadratic equation

x = [12 +/- sqrt(144 - 84)]/2

= 6 +/- sqrt(15)

Clearly, there are 2 solutions, since the sqrt is non-zero, and one solution is with the + option and one is with the -. Choice A.