Question 69915
Substitution seems to be the most straightforward way of solving this system:

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

Look at eq (2)
y=-x-2
-y=x+2
-2y=2x+4-----------substitute this into (1) and we get:


x+2x+4=-8  subtract 4 from both sides
3x=-8-4
3x=-12  divide both sides by 3
x=-4

substitute x=-4 into (2) and we get:

y=4-2
y=2

CK

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

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

Another approach, similar to what you were doing, is as follows:

(1)    x-2y=-8
(2)    y=-x -2 re-arrange by subtracting y and adding 2 to both sides:

(1)    x-2y=-8
(2)    y-y+2=-x-y-2+2  collecting like terms: 

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

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


Add (1) and (2)
-3y=-6  divide both sides by -3
y=2

substitute y=2 in (1)
x-2*2=-8
x-4=-8  add 4 to both sides
x=-4


Hope this helps-----ptaylor