Answer
The solution is $(4,5)$.
Work Step by Step
The given system of equations is
$5x+6y=50$ ...... (1)
$x-6y=-26$ ...... (2)
Add equation (1) and (2).
$\Rightarrow 5x+6y+x-6y=50-26$
Add like terms.
$\Rightarrow 6x=24$
Divide each side by $6$.
$\Rightarrow \frac{6x}{6}=\frac{24}{6}$
Simplify.
$\Rightarrow x=4$
Substitute $4$ for $x$ equation (1).
$\Rightarrow 5(4)+6y=50$
Simplify.
$\Rightarrow 20+6y=50$
Subtract $20$ from each side.
$\Rightarrow 20+6y-20=50-20$
Simplify.
$\Rightarrow 6y=30$
Divide each side by $6$.
$\Rightarrow \frac{6y}{6}=\frac{30}{6}$
Simplify.
$\Rightarrow y=5$
Check $(x,y)=(4,5)$
Equation (1):
$\Rightarrow 5x+6y=50$
$\Rightarrow 5(4)+6(5)=50$
$\Rightarrow 20+30=50$
$\Rightarrow 50=50$
True.
Equation (2):
$\Rightarrow x-6y=-26$
$\Rightarrow 4-6(5)=-26$
$\Rightarrow 4-30=-26$
$\Rightarrow -26=-26$
True.
Hence, the solution is $(4,5)$.
