Solve the System of Equations: 5x+y=21 and x-y=3

$\begin{cases}5x+y=21 \\ x-y=3\end{cases}$

To solve the system of equations:

$5x+y=21$

$x - y = 3$

Let's solve the second equation for $x$:

$x = y + 3$

Substitute $x = y + 3$ into the first equation:

$5(y + 3) + y = 21$

Simplify:

$5y + 15 + y = 21$

$6y = 6$

$y = 1$

Now, substitute $y = 1$ back into $x = y + 3$:

$x = 1 + 3$

$x = 4$

Thus, the solution is $x = 4$, $y = 1$.