Answer
The solution is $(-2,-3)$.
Work Step by Step
The given system of equations is
$\Rightarrow 3x+y=-9$ ...... (1)
$\Rightarrow y=5x+7$ ...... (2)
Substitute $5x+7$ for $y$ in equation (1).
$\Rightarrow 3x+5x+7=-9$
Add like terms.
$\Rightarrow 8x+7=-9$
Subtract $7$ from each side.
$\Rightarrow 8x+7-7=-9-7$
Simplify.
$\Rightarrow 8x=-16$
Divide each side by $8$.
$\Rightarrow \frac{8x}{8}=-\frac{16}{8}$
Simplify.
$\Rightarrow x=-2$
Substitute $-2$ for $x$ in equation (2).
$\Rightarrow y=5(-2)+7$
Simplify.
$\Rightarrow y=-10+7$
$\Rightarrow y=-3$
Check $(x,y)=(-2,-3)$
Equation (1)
$\Rightarrow 3x+y=-9$
$\Rightarrow 3(-2)-3=-9$
$\Rightarrow -6-3=-9$
$\Rightarrow -9=-9$
True.
Equation (2)
$\Rightarrow y=5x+7$
$\Rightarrow -3=5(-2)+7$
$\Rightarrow -3=-10+7$
$\Rightarrow -3=-3$
True.
Hence, the solution is $(-2,-3)$.
