Question

What are the x-coordinates of the solutions to this system of equations? x2 + y2 = 100 y = x + 2

Answer 1

Answer:

x = - 8, x = 6

Step-by-step explanation:

Given the 2 equations

x² + y² = 100 → (1)

y = x + 2 → (2)

Substitute y = x + 2 into (1)

x² + (x + 2)² = 100

x² + x² + 4x + 4 = 100

2x² + 4x + 4 = 100 ( subtract 100 from both sides )

2x² + 4x - 96 = 0 ( divide through by 2 )

x² + 2x - 48 = 0 ← in standard form

(x + 8)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6