23. How many solutions are there to the system of equations below?

y = x2 + 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.

There are exactly 4 solutions

Step-by-step explanation

Given the two equation

y = x² + 3x - 7 ... (1)

y - 5x + 8 = 0 ... (2)

From equation 2,

y - 5x = - 8

y = - 8+5x ... (3)

Substituting equation 3 into 1

-8+5x = x²+3x-7

Moving - 8+5x to the other side of the equation, we have:

x²+3x-7+8-5x = 0

x²+3x-8x-7+8 = 0

x²-5x+1 = 0

Since the resulting equation is quadratic, we will get two solutions as our x and substituting both value of x in equation 2 to get y will give us two solutions for our y variable making a total of 4 solutions.

Therefore in the system of equation given, there are exactly 4 solutions

D

When you add 2+3 which equals 5 so it'll be y=5x-7. And plug in y into the other equation. 5x-7-5x+8=0. - 7-8=0, - 7-8 = -1 therefore there is no solution because-7-8 = - 1 not 0.