Question

solve the following system by graphing.
y = x^2 + 5x + 8
y = -x + 3
select the correct choice and fill in any answer boxes in your choice below.
○ a. the solution(s) is/are
(type an ordered pair. use a comma to separate answers as needed.)
○ b. there is no solution.

Explanation:

Step1: Set the two equations equal.

$x^{2}+5x + 8=-x + 3$

Step2: Rearrange to standard quadratic form.

$x^{2}+5x+x + 8 - 3=0$
$x^{2}+6x + 5=0$

Step3: Factor the quadratic equation.

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

Step4: Solve for x.

If $x+1 = 0$, then $x=-1$; if $x + 5=0$, then $x=-5$

Step5: Find corresponding y - values.

When $x=-1$, $y=-(-1)+3=4$
When $x=-5$, $y=-(-5)+3=8$

Answer:

A. The solution(s) is/are $(-1,4),(-5,8)$