Question

y = x^{2}+8x + 9
y = x + 9
what is a solution (x, y) to the given system of equations?
a (0, -7)
b (0, 9)
c (-7, 0)
d (9, 0)

Explanation:

Step1: Set the two equations equal

Since $y = x^{2}+8x + 9$ and $y=x + 9$, we set $x^{2}+8x + 9=x + 9$.

Step2: Rearrange the equation

Subtract $x$ and 9 from both sides: $x^{2}+8x + 9-(x + 9)=0$, which simplifies to $x^{2}+8x + 9 - x-9=0$, then $x^{2}+7x=0$.

Step3: Factor the equation

Factor out an $x$: $x(x + 7)=0$.

Step4: Solve for $x$

Using the zero - product property, if $x(x + 7)=0$, then $x=0$ or $x=-7$.

Step5: Find the corresponding $y$ values

When $x = 0$, substitute into $y=x + 9$, we get $y=0 + 9=9$.
When $x=-7$, substitute into $y=x + 9$, we get $y=-7 + 9=2$.
The solution $(0,9)$ is among the options.

Answer:

B. $(0,9)$