Question

Find the solutions to the system:
y = x^2 - 5x +2
y = -6x +4
a. (2, 8) and (-1, 2)
b. (-2, 8) and (1, -2)
c. (-2, 16) and (1, -2)
d. no solutions

Answer 1

The correct answer for the question that is being presented above is this one: "d. no solutions." The solutions to the system is this:d. no solutions
y = x^2 - 5x +2 (2,8)
y = 4 - 10 + 2
y = 8

y = x^2 - 5x +2 (-1,2)
y = 1 + 10 + 2
y = 13

y = -6x +4 (2,8)
y = -6(2) + 4
y = 8

y = -6x +4 (-1,2)
y = -6(-1) + 4
y = 2

Answer 2

y = x² - 5x + 2
y = -6x + 4

-6x + 4 = x² - 5x + 2
0 = x² - 5x + 2 + 6x - 4
0 = x² + x - 2

(x + 2)(x - 1)

x = -2 ; x = 1

y = x² - 5x + 2 ; x = -2                  y = x² - 5x + 2 ; x = 1
y = (-2)² - 5(-2) + 2                      y = 1² - 5(1) + 2
y = 4 + 10 + 2                              y = 1 - 5 + 2
y = 16                                          y = -2

y = -6x + 4 ; x = -2                       y = -6x + 4 ; x = 1
y = -6(-2) + 4                               y = -6(1) + 4 
y = 12 + 4                                    y = -6 + 4
y = 16                                          y = -2

Choice C. (-2, 16) and (1, -2) is the answer.