Question

What are the solutions to the following system of equations?

2x − y = 6
y = x2 − 9

Answer 1

(3, 0) and (-1, -8)

Explanation:

Equation 1

• 2x - y = 6
• Rearrange it so that it is equal to 'y'
• -y = 6 - 2x
• y = 2x - 6

Substituting the value of y in Equation 2

• y = x² - 9
• ⇒ 2x - 6 = x² - 9
• ⇒ x² - 2x - 3 = 0
• ⇒ x² + x - 3x - 3 = 0
• ⇒ x(x + 1) - 3(x + 1) = 0
• ⇒ (x - 3)(x + 1) = 0
• ⇒ x = 3, -1

Taking x = 3

• y = 2(3) - 6
• y = 0
• Solution 1 = (3, 0)

Taking x = -1

• y = 2(-1) - 6
• y = -2 - 6
• y = -8
• Solution 2 = (-1, -8)

Solutions

• (3, 0) and (-1, -8)