Question

4.9.14
Solve the following system by substitution.
{
y = x2 + 6x + 10
y = -X+4
Select the correct choice and fill in any answer

- the solution(s) is/are :
- there is no solution

Answer 1

Answer:

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

Step-by-step explanation:

Given the 2 equations

y = x² + 6x + 10 → (1)

y = - x + 4 → (2)

Substitute y =  x² + 6x + 10 into (2)

x² + 6x + 10 = - x + 4 ( subtract - x + 4 from both sides )

x² + 7x + 6 = 0 ← in standard form

(x + 1)(x + 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x + 6 = 0 ⇒ x = - 6

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

x = - 1 : y = - (- 1) + 4 = 1 + 4 = 5 ⇒ (- 1, 5 )

x = - 6 : y = - (- 6) + 4 = 6 + 4 = 10 ⇒ (- 6, 10 )