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7 June, 06:21

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.

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Answers (2)
  1. 7 June, 06:27
    0
    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
  2. 7 June, 07:58
    0
    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.
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