Question

Find the solution to the system

y=x^2+8x+2
y=7x+4

A(-2,-10) and (1,11)
B(2,10) and (-1,-11)
C(-2,-34) and (1,11)
D no solution

Answer 1

A

Explanation:

Given the 2 equations

y = x² + 8x + 2 → (1)

y = 7x + 4 → (2)

Substitute y = x² + 8x + 2 into (2)

x² + 8x + 2 = 7x + 4 ( subtract 7x + 4 from both sides )

x² + x - 2 = 0 ← in standard form

(x + 2)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 1 = 0 ⇒ x = 1

Substitute these values into (2) for the corresponding values of y

x = - 2 : y = - 14 + 4 = - 10 ⇒ (- 2, - 10)

x = 1 : y = 7 + 4 = 11 ⇒ (1, 11)

The solutions are (- 2, - 10) and (1, 11) → A