Answer
The solution is $(2,2)$.
Work Step by Step
The given system of equations is
$6x+2y=16$ ...... (1)
$2x-y=2$ ...... (2)
Multiply equation (2) by $2$.
$2(2x-y)=2(2)$
Use distributive property.
$4x-2y=4$ ...... (3)
Add equation (1) and (3).
$\Rightarrow 6x+2y+4x-2y=16+4$
Add like terms.
$\Rightarrow 10x=20$
Divide each side by $10$.
$\Rightarrow \frac{10x}{10}=\frac{20}{10}$
Simplify.
$\Rightarrow x=2$
Substitute $2$ for $x$ in equation (1).
$\Rightarrow 6(2)+2y=16$
Simplify.
$\Rightarrow 12+2y=16$
Subtract $12$ from each side.
$\Rightarrow 12+2y-12=16-12$
Simplify.
$\Rightarrow 2y=4$
Divide each side by $2$.
$\Rightarrow \frac{2y}{2}=\frac{4}{2}$
Simplify.
$\Rightarrow y=2$
Hence, the solution is $(2,2)$.
