Answer
The solution is $(-3,1)$.
Work Step by Step
The given system of equations is
$4x-9y=-21$ ...... (1)
$-4x-3y=9$ ...... (2)
Add equation (1) and (2).
$\Rightarrow 4x-9y-4x-3y=-21+9$
Add like terms.
$\Rightarrow -12y=-12$
Divide each side by $-12$.
$\Rightarrow \frac{-12y}{-12}=\frac{-12}{-12}$
Simplify.
$\Rightarrow y=1$
Substitute $1$ for $y$ in equation (1).
$\Rightarrow 4x-9(1)=-21$
Simplify.
$\Rightarrow 4x-9=-21$
Add $9$ to each side.
$\Rightarrow 4x-9+9=-21+9$
Simplify.
$\Rightarrow 4x=-12$
Divide each side by $4$.
$\Rightarrow \frac{4x}{4}=\frac{-12}{4}$
Simplify.
$\Rightarrow x=-3$
Check $(x,y)=(-3,1)$
Equation (1):
$\Rightarrow 4x-9y=-21$
$\Rightarrow 4(-3)-9(1)=-21$
$\Rightarrow -12-9=-21$
$\Rightarrow -21=-21$
True.
Equation (2):
$\Rightarrow -4x-3y=9$
$\Rightarrow -4(-3)-3(1)=9$
$\Rightarrow 12-3=9$
$\Rightarrow 9=9$
True.
Hence, the solution is $(-3,1)$.
