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