Answer
The solution is $(8,3)$.
Work Step by Step
The given system of equations is
$11x-20y=28$ ...... (1)
$3x+4y=36$ ...... (2)
Multiply each side of equation (2) by $5$.
$5(3x+4y)=5(36)$
Simplify.
$15x+20y=180$ ...... (3)
Add equation (1) and (3).
$\Rightarrow 11x-20y+15x+20y=28+180$
Add like terms.
$\Rightarrow 26x=208$
Divide each side by $26$.
$\Rightarrow \frac{26x}{26}=\frac{208}{26}$
Simplify.
$\Rightarrow x=8$
Substitute $8$ for $x$ in equation (2).
$\Rightarrow 3(8)+4y=36$
Simplify.
$\Rightarrow 24+4y=36$
Subtract $24$ from each side.
$\Rightarrow 24+4y-24=36-24$
Simplify.
$\Rightarrow 4y=12$
Divide each side by $4$.
$\Rightarrow \frac{4y}{4}=\frac{12}{4}$
Simplify.
$\Rightarrow y=3$
Check $(x,y)=(8,3)$
Equation (1):
$\Rightarrow 11x-20y=28$
$\Rightarrow 11(8)-20(3)=28$
$\Rightarrow 88-60=28$
$\Rightarrow 28=28$
True.
Equation (2):
$\Rightarrow 3x+4y=36$
$\Rightarrow 3(8)+4(3)=36$
$\Rightarrow 24+12=36$
$\Rightarrow 36=36$
True.
Hence, the solution is $(8,3)$.
