We are given a system of two linear equations with two variables, $x$ and $y$. We need to solve for $x$ and $y$. The system of equations is: $-8x + 4y = 0$ $x + 6y = -13$

1. Problem Description

We are given a system of two linear equations with two variables, $x$ and $y$. We need to solve for $x$ and $y$. The system of equations is:

$-8x + 4y = 0$

$x + 6y = -13$

2. Solution Steps

We can solve this system of equations using either substitution or elimination. Let's use elimination.

First, multiply the second equation by 8 to eliminate $x$:

$8(x + 6y) = 8(-13)$

$8x + 48y = -104$

Now we have the two equations:

$-8x + 4y = 0$

$8x + 48y = -104$

Add the two equations together:

$(-8x + 4y) + (8x + 48y) = 0 + (-104)$

$52y = -104$

Divide both sides by 52:

$y = \frac{-104}{52}$

$y = -2$

Now that we have the value of $y$, we can substitute it into either equation to solve for $x$. Let's use the second equation:

$x + 6y = -13$

$x + 6(-2) = -13$

$x - 12 = -13$

$x = -13 + 12$

$x = -1$

So, we have $x = -1$ and $y = -2$.

3. Final Answer

$x = -1$

$y = -2$

Final Answer: $x = -1, y = -2$