Answer
$\left\{\left (7,\frac{1}{3}\right)\right\}$.
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
3x& +12y&=&25& ...... (1) \\
2x& -6y &=&12& ...... (2)
\end{matrix}\right.$
Addition method:-
Multiply the equation (2) by $2$.
$\Rightarrow 4x-12y =24 $ ...... (3)
Add equation (1) and (3).
$\Rightarrow 3x+12y+4x-12y =25+24 $
Simplify.
$\Rightarrow 7x =49$
Divide both sides by $7$.
$\Rightarrow \frac{7x}{7} =\frac{49}{7}$
Simplify.
$\Rightarrow x =7$
Substitute $x=7$ into the equation (1).
$\Rightarrow 3(7) +12y=25 $
$\Rightarrow 21 +12y=25 $
Subtract $21$ from both sides.
$\Rightarrow 21 +12y-21=25-21 $
Add like terms.
$\Rightarrow 12y=4 $
Divide both sides by $12$.
$\Rightarrow \frac{12y}{12}=\frac{4}{12} $
Simplify.
$\Rightarrow y=\frac{1}{3} $
The solution set is $\{(x,y)\}=\left\{\left (7,\frac{1}{3}\right)\right\}$.
