Answer
The solution is $(12,6)$.
Work Step by Step
The given system of equations is
$3x-30=y$ ...... (1)
$7y-6=3x$ ...... (2)
Add equation (1) and (2).
$\Rightarrow 3x-30+7y-6=y+3x$
Add like terms.
$\Rightarrow 3x-36+7y=y+3x$
Add $-3x-y+36$ to each side.
$\Rightarrow 3x-36+7y-3x-y+36=y+3x-3x-y+36$
Simplify.
$\Rightarrow 6y=36$
Divide each side by $6$.
$\Rightarrow \frac{6y}{6}=\frac{36}{6}$
Simplify.
$\Rightarrow y=6$
Substitute $6$ for $y$ in equation (1).
$\Rightarrow 3x-30=6$
Add $30$ to each side.
$\Rightarrow 3x-30+30=6+30$
Simplify.
$\Rightarrow 3x=36$
Divide each side by $3$.
$\Rightarrow \frac{3x}{3}=\frac{36}{3}$
Simplify.
$\Rightarrow x=12$
Check $(x,y)=(12,6)$
Equation (1):
$\Rightarrow 3x-30=y$
$\Rightarrow 3(12)-30=6$
$\Rightarrow 36-30=6$
$\Rightarrow 6=6$
True.
Equation (2):
$\Rightarrow 7y-6=3x$
$\Rightarrow 7(6)-6=3(12)$
$\Rightarrow 42-6=36$
$\Rightarrow 36=36$
True.
Hence, the solution is $(12,6)$.
