Y = x2 + 4x + 4
y = 2x + 7

How many solutions?

2 solutions

Step-by-step explanation:

Given the 2 equations

y = x² + 4x + 4 → (1)

y = 2x + 7 → (2)

Substitute y = x² + 4x + 4 into (2)

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

x² + 2x - 3 = 0 ← in standard form

(x + 3)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 1 = 0 ⇒ x = 1

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

x = - 3 : y = 2(- 3) + 7 = - 6 + 7 = 1 ⇒ (- 3, 1 )

x = 1 : y = 2(1) + 7 = 2 + 7 = 9 ⇒ (1, 9 )

The 2 solutions are (- 3, 1 ) and (1, 9 )