Answer
$\{(-5,2)\}$.
Work Step by Step
We will use the Elimination Method to solve the given system of equations:
$\Rightarrow 3x+4y=-7$ ...... (1)
$\Rightarrow x-2y=-9$ ...... (2)
Multiply equation (2) by $-3$.
$\Rightarrow -3(x-2y)=-3(-9)$
Simplify.
$\Rightarrow -3x+6y=27$ ...... (3)
Add equation (1) and (3).
$\Rightarrow 3x+4y-3x+6y=-7+27$
Simplify.
$\Rightarrow 10y=20$
Divide both sides by $10$.
$\Rightarrow \frac{10y}{10}=\frac{20}{10}$
Simplify.
$\Rightarrow y=2$
Substitute the value of $y$ into equation (2).
$\Rightarrow x-2(2)=-9$
Simplify.
$\Rightarrow x-4=-9$
Add both sides $4$.
$\Rightarrow x-4+4=-9+4$
Simplify.
$\Rightarrow x=-5$
Hence, the solution set is $\{(-5,2)\}$.
