Solve the system of equations: { x - 2y = -8, x/4 + (y-2)/3 = -1 }

Step 1: Simplify the second equation by multiplying by the least common multiple of 4 and 3, which is 12.

12 * (x/4 + (y-2)/3) = 12 * (-1)

3x + 4(y-2) = -12

3x + 4y - 8 = -12

3x + 4y = -4

Step 2: Now we have a system of two linear equations:

1) x - 2y = -8

2) 3x + 4y = -4

Step 3: Solve the first equation for x: x = 2y - 8.

Step 4: Substitute this expression for x into the second equation:

3(2y - 8) + 4y = -4

6y - 24 + 4y = -4

10y = 20

y = 2

Step 5: Substitute the value of y back into the equation for x:

x = 2(2) - 8

x = 4 - 8

x = -4

Solution: x = -4, y = 2