Substitution Method Challenge: Solve for x and y in the System -x-2y=4, 3x+y=8

Find the value of x and and band the substitution method.

$\begin{cases} -x-2y=4 \\ 3x+y=8 \end{cases}$

Let's begin by solving the system of equations using the substitution method.

First, solve the second equation for $y$:

$3x + y = 8$

Solve for $y$:

$y = 8 - 3x$

Next, substitute this expression for $y$ in the first equation:

$-x - 2(8 - 3x) = 4$

Distribute the $-2$:

$-x - 16 + 6x = 4$

Combine like terms:

$5x - 16 = 4$

Add 16 to both sides:

$5x = 20$

Divide by 5:

$x = 4$

Now, substitute $x = 4$ back into $y = 8 - 3x$ to find $y$:

$y = 8 - 3(4)$

$y = 8 - 12$

$y = -4$

Therefore, the solution to the system of equations is $(x, y) = (4, -4)$.

Thus, the values of $x$ and $y$ are $x = 4$ and $y = -4$.