Answer
The solution is $(6,1)$.
Work Step by Step
The given system of equations is
$\Rightarrow 3x-5y=13$ ...... (1)
$\Rightarrow x+4y=10$ ...... (2)
Subtract $4y$ from each side of equation (2).
$\Rightarrow x+4y-4y=10-4y$
$\Rightarrow x=-4y+10$ ...... (3)
Substitute $-4y+10$ for $x$ in equation (1).
$\Rightarrow 3(-4y+10)-5y=13$
Use distributive property.
$\Rightarrow -12y+30-5y=13$
Add like terms.
$\Rightarrow -17y+30=13$
Add $17y-13$ to each side.
$\Rightarrow -17y+30+17y-13=13+17y-13$
Simplify.
$\Rightarrow 17=17y$
Divide each side by $17$.
$\Rightarrow \frac{17}{17}=\frac{17y}{17}$
Simplify.
$\Rightarrow 1=y$
Substitute $1$ for $y$ in equation (2).
$\Rightarrow x+4(1)=10$
Simplify.
$\Rightarrow x+4=10$
Subtract $4$ from each side.
$\Rightarrow x+4-4=10-4$
Simplify.
$\Rightarrow x=6$
Check: $(x,y)=(6,1)$
Equation (1)
$\Rightarrow 3x-5y=13$
$\Rightarrow 3(6)-5(1)=13$
$\Rightarrow 18-5=13$
$\Rightarrow 13=13$
True.
Equation (2)
$\Rightarrow x+4y=10$
$\Rightarrow 6+4(1)=10$
$\Rightarrow 6+4=10$
$\Rightarrow 10=10$
True.
Hence, the solution is $(6,1)$.
