Answer
The solution is $(4,-1)$.
Work Step by Step
The given system of equations is
$x+3y=1$ ...... (1)
$5x+6y=14$ ...... (2)
Multiply equation (1) by $-2$.
$-2(x+3y)=-2(1)$
Use distributive property.
$-2x-6y=-2$ ...... (3)
Add equation (2) and (3).
$\Rightarrow 5x+6y-2x-6y=14-2$
Add like terms.
$\Rightarrow 3x=12$
Divide each side by $3$.
$\Rightarrow \frac{3x}{3}=\frac{12}{3}$
Simplify.
$\Rightarrow x=4$
Substitute $4$ for $x$ in equation (1).
$\Rightarrow 4+3y=1$
Subtract $4$ from each side.
$\Rightarrow 4+3y-4=1-4$
Simplify.
$\Rightarrow 3y=-3$
Divide each side by $3$.
$\Rightarrow \frac{3y}{3}=\frac{-3}{3}$
Simplify.
$\Rightarrow y=-1$
Check $(x,y)=(4,-1)$
Equation (1):
$\Rightarrow x+3y=1$
$\Rightarrow 4+3(-1)=1$
$\Rightarrow 4-3=1$
$\Rightarrow 1=1$
True.
Equation (2):
$\Rightarrow 5x+6y=14$
$\Rightarrow 5(4)+6(-1)=14$
$\Rightarrow 20-6=14$
$\Rightarrow 14=14$
True.
Hence, the solution is $(4,-1)$.
