Answer
The solution is $(-7,-12)$.
Work Step by Step
The given system of equations is
$4x-3y=8$ ...... (1)
$5x-2y=-11$ ...... (2)
Multiply each side of equation (1) by $-2$.
$-2(4x-3y)=-2(8)$
Simplify.
$-8x+6y=-16$ ...... (3)
Multiply each side of equation (2) by $3$.
$3(5x-2y)=3(-11)$
Simplify.
$15x-6y=-33$ ...... (4)
Add equation (3) and (4).
$\Rightarrow -8x+6y+15x-6y=-16-33$
Add like terms.
$\Rightarrow 7x=-49$
Divide each side by $7$.
$\Rightarrow \frac{7x}{7}=\frac{-49}{7}$
Simplify.
$\Rightarrow x=-7$
Substitute $-7$ for $x$ in equation (1).
$\Rightarrow 4(-7)-3y=8$
Simplify.
$\Rightarrow -28-3y=8$
Add $28$ to each side.
$\Rightarrow -28-3y+28=8+28$
Simplify.
$\Rightarrow -3y=36$
Divide each side by $-3$.
$\Rightarrow \frac{-3y}{-3}=\frac{36}{-3}$
Simplify.
$\Rightarrow y=-12$
Check $(x,y)=(-7,-12)$
Equation (1):
$\Rightarrow 4x-3y=8$
$\Rightarrow 4(-7)-3(-12)=8$
$\Rightarrow -28+36=8$
$\Rightarrow 8=8$
True.
Equation (2):
$\Rightarrow 5x-2y=-11$
$\Rightarrow 5(-7)-2(-12)=-11$
$\Rightarrow -35+24=-11$
$\Rightarrow -11=-11$
True.
Hence, the solution is $(-7,-12)$.
