Answer
The solution is $(-1,-3)$.
Work Step by Step
The given system is
$y=-3x^2$ ...... (1)
$y=6x+3$ ...... (2)
Substitute $6x+3$ for $y$ in equation (1).
$\Rightarrow 6x+3=-3x^2$
Add $3x^2$ to each side.
$\Rightarrow 6x+3+3x^2=-3x^2+3x^2$
Simplify.
$\Rightarrow 3x^2+6x+3=0$
Divide each side by $3$.
$\Rightarrow x^2+2x+1=0$
Write the left side as the square of a binomial.
$\Rightarrow (x+1)^2=0$
Take square root on each side.
$\Rightarrow x+1=0$
Solve for $x$.
$\Rightarrow x=-1$
Substitute $-1$ for $x$ in equation (2).
$\Rightarrow y=6(-1)+3$
Simplify.
$\Rightarrow y=-6+3$
$\Rightarrow y=-3$
Hence, the solution is $(-1,-3)$.
