Question

What are the solutions to the following system of equations?

2x − y = 6
y = x2 − 9

(3, 0) and (−1, −8)
(3, 0) and (4, 2)
(−3, 0) and (−1, −8)
(−3, 0) and (4, 2)

Answer 1

(3, 0) and (−1, −8)

Equation's:

• 2x − y = 6

• y = x² − 9

Substitute equation 2 into 1

2x − (x² − 9) = 6

2x - x² + 9 = 6

-x² + 2x + 9 - 6 = 0

-x² + 2x + 3 = 0

x² - 2x - 3 = 0

x² - 3x + x - 3 = 0

x(x - 3) + 1(x - 3) = 0

(x + 1)(x - 3) = 0

x = -1, x = 3

Find values for y

If x = -1, then y = (-1)² - 9 = -8

If x = 3, then y = (3)² - 9 = 0

Solution Set:

(x, y) = (-1, -8), (3, 0)