Answer
The solutions are $(-3,15)$ and $(1,-5)$.
Work Step by Step
The given system is
$y=-5x$ ...... (1)
$y=x^2-3x-3$ ...... (2)
Substitute $-5x$ for $y$ in equation (2).
$\Rightarrow -5x=x^2-3x-3$
Add $5x$ to each side.
$\Rightarrow -5x+5x=x^2-3x-3+5x$
Simplify.
$\Rightarrow 0=x^2+2x-3$
Factor the polynomial.
$\Rightarrow 0=(x+3)(x-1)$
Use zero product property.
$\Rightarrow x+3=0$ or $x-1=0$
Solve for $x$.
$\Rightarrow x=-3$ or $x=1$
Substitute $-3$ for $x$ in equation (1).
$\Rightarrow y=-5(-3)$
Simplify.
$\Rightarrow y=15$
Substitute $1$ for $x$ in equation (1).
$\Rightarrow y=-5(1)$
Simplify.
$\Rightarrow y=-5$
Hence, the solutions are $(-3,15)$ and $(1,-5)$.
