SOLUTION: please help answer this systems of equations: substitution and elimination method , please show all work. y = -4x-8 -8x-4y = -8

y = -4x - 8      (1)
-8x - 4y = -8    (2)

You just have y expressed via x in the equation (1).
So, simply substitute this expression for y into the equation (2).
You will get a single equation for x:

-8x - 4*(-4x - 8) = -8.    (3)

Simplify and solve it:

-8x +16x + 32 = -8,

8x + 32 = -8,
8x = -8 - 32,
8x = -40,

x =  = .

Then, according to (1), y = -4x - 8 = -4*(-5) - 8 = 20 - 8 = 12.

Answer.  x = -5, y = 12.

Rewrite your original system in an equivalent form

 4x +  y = -8    (1')
-8x - 4y = -8    (2')

Now multiply the equation (1') by 2 and add to the equation (2'). 
In this way you eliminate the unknown x and get a single equation for the unknown y:

2y - 4y = -16 - 8.

Simplify it:

-2y = -24,

y =  = 12.

Then from (1') 4x = -8 -y = -8 - 12 = -20 and x =  = -5.

Thus you got the same answer.