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