4.9.18

Solve the following system by substitution.

y = x2 + 5x + 10

y = - X+5

Select the correct choice and fill in any answer boxes in

- the solution (s) is/are:

- there is no solution

x = - 5 or - 1

Step-by-step explanation:

subst y = - x + 5 into y = x^2 + 5x + 10

-x + 5 = x^2 + 5x + 10

x^2 + 6x + 5 = 0

(x+5) (x+1) = 0

x = - 5 or - 1

( - 5, 10) and ( - 1, 6)

Step-by-step explanation:

Given the 2 equations

y = x² + 5x + 10 → (1)

y = - x + 5 → (2)

Substitute y = x² + 5x + 10 into (2)

x² + 5x 6 + 10 = - x + 5 (subtract - x + 5 from both sides)

x² + 6x + 5 = 0 ← in standard form

(x + 1) (x + 5) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x + 5 = 0 ⇒ x = - 5

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

x = - 5 : y = - ( - 5) + 5 = 5 + 5 = 10 ⇒ ( - 5, 10)

x = - 1 : y = - ( - 1) + 5 = 1 + 5 = 6 ⇒ ( - 1, 6)