Answer
The solution is $(-17,5)$.
Work Step by Step
The given system of equations is
$-2x-5y=9$ ...... (1)
$3x+11y=4$ ...... (2)
Multiply each side of equation (1) by $3$.
$3(-2x-5y)=3(9)$
Simplify.
$-6x-15y=27$ ...... (3)
Multiply each side of equation (2) by $2$.
$2(3x+11y)=2(4)$
Simplify.
$6x+22y=8$ ...... (4)
Add equation (3) and (4).
$\Rightarrow -6x-15y+6x+22y=27+8$
Add like terms.
$\Rightarrow 7y=35$
Divide each side by $7$.
$\Rightarrow \frac{7y}{7}=\frac{35}{7}$
Simplify.
$\Rightarrow y=5$
Substitute $5$ for $y$ in equation (2).
$\Rightarrow 3x+11(5)=4$
Simplify.
$\Rightarrow 3x+55=4$
Subtract $55$ from each side.
$\Rightarrow 3x+55-55=4-55$
Simplify.
$\Rightarrow 3x=-51$
Divide each side by $3$.
$\Rightarrow \frac{3x}{3}=\frac{-51}{3}$
Simplify.
$\Rightarrow x=-17$
Check $(x,y)=(-17,5)$
Equation (1):
$\Rightarrow -2x-5y=9$
$\Rightarrow -2(-17)-5(5)=9$
$\Rightarrow 34-25=9$
$\Rightarrow 9=9$
True.
Equation (2):
$\Rightarrow 3x+11y=4$
$\Rightarrow 3(-17)+11(5)=4$
$\Rightarrow -51+55=4$
$\Rightarrow 4=4$
True.
Hence, the solution is $(-17,5)$.
