We are given a system of two linear equations with two variables, $x$ and $y$: $5x + 4y = -8$ $x + 4y = 8$ We need to find the values of $x$ and $y$ that satisfy both equations.

1. Problem Description

We are given a system of two linear equations with two variables, $x$ and $y$:

$5x + 4y = -8$

$x + 4y = 8$

We need to find the values of $x$ and $y$ that satisfy both equations.

2. Solution Steps

We can solve this system using the method of elimination. Notice that the coefficients of $y$ in both equations are the same (4). Therefore, we can subtract the second equation from the first equation to eliminate $y$.

$(5x + 4y) - (x + 4y) = -8 - 8$

$5x + 4y - x - 4y = -16$

$4x = -16$

Now, we can solve for $x$ by dividing both sides by 4:

$x = \frac{-16}{4}$

$x = -4$

Next, we substitute the value of $x$ into either of the original equations to solve for $y$. Let's use the second equation:

$x + 4y = 8$

$-4 + 4y = 8$

Add 4 to both sides:

$4y = 8 + 4$

$4y = 12$

Divide both sides by 4:

$y = \frac{12}{4}$

$y = 3$

Therefore, the solution is $x = -4$ and $y = 3$.

3. Final Answer

$x = -4, y = 3$