For the first equation:
4.7 - 1.1x = 0.5x - 3.37

First, let's simplify by combining like terms:

Add 1.1x to both sides:
4.7 = 1.6x - 3.37

Add 3.37 to both sides:
4.7 + 3.37 = 1.6x
8.07 = 1.6x

Divide by 1.6 to solve for x:
x = 8.07 / 1.6
x = 5.04375

Now for the second equation:
8x - 8 = 20 - 6x

Add 6x to both sides:
8x + 6x - 8 = 20

Simplify:
14x - 8 = 20

Add 8 to both sides:
14x = 28

Divide by 14 to solve for x:
x = 28 / 14
x = 2

Therefore, the solutions to the system of equations are x = 5.04375 and x = 2.