Question

How many solutions are there to the systems of equations below? (PLEASE ANSWER + 10 POINTS!!!)

y = x^2 + 3x - 7
y - 5x + 8 = 0

A. There are exactly 4 solutions.

B. There are exactly 2 solutions.

C. There is exactly 1 solution.

D. There are no solutions.

Answer 1

The answer to the question is c

Answer 2

y = x² + 3x - 7

y - 5x + 8 → y = 5x - 8

5x - 8 = x² + 3x - 7 substituted "y" in first equation with "5x - 8"

0 = x² - 2x + 1 subtracted 5x and added 8 to both sides

0 = (x -1)(x - 1) factored x² - 2x + 1

x = 1 solved for "x"

Now plug that "x = 1" into "y = 5x - 8" → y = 5(1) - 8 → y = 5 - 8 → y = -3

Solution is (1, -3) so there is only one solution.

Answer: C