Answer
The solution is $(6,-6)$.
Work Step by Step
The given system of equations is
$x-3y=24$ ...... (1)
$3x+y=12$ ...... (2)
Multiply equation (2) by $3$.
$3(3x+y)=3(12)$
Use distributive property.
$9x+3y=36$ ...... (3)
Add equation (1) and (3).
$\Rightarrow x-3y+9x+3y=24+36$
Add like terms.
$\Rightarrow 10x=60$
Divide each side by $10$.
$\Rightarrow \frac{10x}{10}=\frac{60}{10}$
Simplify.
$\Rightarrow x=6$
Substitute $6$ for $x$ equation (2).
$\Rightarrow 3(6)+y=12$
Simplify.
$\Rightarrow 18+y=12$
Subtract $18$ from each side.
$\Rightarrow 18+y-18=12-18$
Simplify.
$\Rightarrow y=-6$
Check $(x,y)=(6,-6)$
Equation (1):
$\Rightarrow x-3y=24$
$\Rightarrow 6-3(-6)=24$
$\Rightarrow 6+18=24$
$\Rightarrow 24=24$
True.
Equation (2):
$\Rightarrow 3x+y=12$
$\Rightarrow 3(6)-6=12$
$\Rightarrow 18-6=12$
$\Rightarrow 12=12$
True.
Hence, the solution is $(6,-6)$.
