To solve the system of equations:

1. $-5x - 2y = -4$
2. $x - 2y = 8$

You can use the elimination method. Let's eliminate $y$:

First, subtract equation 2 from equation 1: $(-5x - 2y) - (x - 2y) = -4 - 8$

This simplifies to: $-5x - 2y - x + 2y = -12$

The $y$ terms cancel out: $-6x = -12$

Now, solve for $x$: $x = \frac{-12}{-6} = 2$

Substitute $x = 2$ back into equation 2: $2 - 2y = 8$

Solve for $y$: $-2y = 8 - 2$ $-2y = 6$ $y = -3$

So, the solution is $x = 2$, $y = -3$.