Answer
The solution is $(3,7)$.
Work Step by Step
The given system of equations is
$3x-2y=-5$ ...... (1)
$4x+5y=47$ ...... (2)
Multiply equation (1) by $5$.
$5(3x-2y)=5(-5)$
Use distributive property.
$15x-10y=-25$ ...... (3)
Multiply equation (2) by $2$.
$2(4x+5y)=2(47)$
Use distributive property.
$8x+10y=94$ ...... (4)
Add equation (3) and (4).
$\Rightarrow 15x-10y+8x+10y=-25+94$
Add like terms.
$\Rightarrow 23x=69$
Divide each side by $23$.
$\Rightarrow \frac{23x}{23}=\frac{69}{23}$
Simplify.
$\Rightarrow x=3$
Substitute $3$ for $x$ in equation (2).
$\Rightarrow 4(3)+5y=47$
Simplify.
$\Rightarrow 12+5y=47$
Subtract $12$ from each side.
$\Rightarrow 12+5y-12=47-12$
Simplify.
$\Rightarrow 5y=35$
Divide each side by $5$.
$\Rightarrow \frac{5y}{5}=\frac{35}{5}$
Simplify.
$\Rightarrow y=7$
Hence, the solution is $(3,7)$.
