Question

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

Answer 1

x= -5 or -1

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

Answer 2

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

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 )