Answer
The solutions are $(4,-11)$ and $(-4,29)$.
Work Step by Step
The given system is
$y=x^2-5x-7$ ...... (1)
$y=-5x+9$ ...... (2)
Subtract equation (2) from equation (1).
$\Rightarrow y-y=x^2-5x-7-(-5x+9)$
Clear the parentheses.
$\Rightarrow y-y=x^2-5x-7+5x-9$
Simplify.
$\Rightarrow 0=x^2-16$
Add $16$ to each side.
$\Rightarrow 0+16=x^2-16+16$
Simplify.
$\Rightarrow 16=x^2$
Take square root on each side.
$\Rightarrow \pm\sqrt{16}=x$
Simplify.
$\Rightarrow \pm4=x$
Substitute $4$ for $x$ in equation (2).
$\Rightarrow y=-5(4)+9$
Simplify.
$\Rightarrow y=-20+9$
$\Rightarrow y=-11$
Substitute $-4$ for $x$ in equation (2).
$\Rightarrow y=-5(-4)+9$
Simplify.
$\Rightarrow y=20+9$
$\Rightarrow y=29$
Hence, the solutions are $(4,-11)$ and $(-4,29)$.
