#### Answer

$x=3$
$y=2$

#### Work Step by Step

$\begin{cases} x-y=1\\4x+3y=18\end{cases}$
Let $x-y=1$ be equation number 1 and $4x+3y=18$ be equation number 2:
Solve for $x$ in equation 1:
$x=1+y$
Let this equation be equation number 3
Substitute equation 3 in equation 2:
$4x+3y=18$
$4(1+y)+3y=18$
$4+4y+3y=18$
Now, solve for $y$:
$7y=18-4$
$7y=14$
$y=\dfrac{14}{7}=2$
Substitute $y=2$ in equation 3:
$x=1+y$
$x=1+2=3$