Answer
The solution is $(5,-3)$.
Work Step by Step
The given system of equations is
$9x+2y=39$ ...... (1)
$6x+13y=-9$ ...... (2)
Multiply each side of equation (1) by $-2$.
$-2(9x+2y)=-2(39)$
Simplify.
$-18x-4y=-78$ ...... (3)
Multiply each side of equation (2) by $3$.
$3(6x+13y)=3(-9)$
Simplify.
$18x+39y=-27$ ...... (4)
Add equation (3) and (4).
$\Rightarrow -18x-4y+18x+39y=-78-27$
Add like terms.
$\Rightarrow 35y=-105$
Divide each side by $35$.
$\Rightarrow \frac{35y}{35}=\frac{-105}{35}$
Simplify.
$\Rightarrow y=-3$
Substitute $-3$ for $y$ in equation (1).
$\Rightarrow 9x+2(-3)=39$
Simplify.
$\Rightarrow 9x-6=39$
Add $6$ to each side.
$\Rightarrow 9x-6+6=39+6$
Simplify.
$\Rightarrow 9x=45$
Divide each side by $9$.
$\Rightarrow \frac{9x}{9}=\frac{45}{9}$
Simplify.
$\Rightarrow x=5$
Check $(x,y)=(5,-3)$
Equation (1):
$\Rightarrow 9x+2y=39$
$\Rightarrow 9(5)+2(-3)=39$
$\Rightarrow 45-6=39$
$\Rightarrow 39=39$
True.
Equation (2):
$\Rightarrow 6x+13y=-9$
$\Rightarrow 6(5)+13(-3)=-9$
$\Rightarrow 30-39=-9$
$\Rightarrow -9=-9$
True.
Hence, the solution is $(5,-3)$.
