System of equations? Four variables

x + a =-4
y + b = 3
2a - b = 0
-x - 2y = 0

x + a = -4 ..... (1)
y + b = 3 ..... (2)
2a - b = 0 ..... (3)
-x - 2y = 0 ....(4)

Using substitution:
Rearrange (1)
x = -4 - a
Rearrange (2)
y = 3 - b

Substitute the above to (4)
- (-4 - a) - 2(3-b) = 0
4 + a - 6 + 2b = 0
a + 2b -2 = 0
a = 2 - 2b

Substitute the above to (3)
2(2 - 2b) - b = 0
4 - 4b - b = 0
4 - 5b = 0
4 = 5b
b = 4/5
b = 0.8

Substitute b to (3)
2a - 4/5 = 0
2a = 4/5
a = 4/10 = 0.4

Substitute a to (1)
x + 0.4 = -4
x = -4 - 0.4
x = -4.4

Substitute b to (2)
y + 0.8 = 3
y = 3 - 0.8
y = 2.2

You can check your answer using the following calculator:
http://www.idomaths.com/simeq.php