The solution to this system is (-2, 1):
To solve the system of linear equations, we can use the method of substitution or elimination. Here, we will use the method of substitution.
From the second equation, we can solve for y in terms of x:
3x + 2y = -6
2y = -3x - 6
y = (-3/2)x - 3
Now we can substitute this expression for y into the first equation:
4x - 3y = -8
4x - 3((-3/2)x - 3) = -8
Simplifying and solving for x, we get:
4x + (9/2)x = 1
(17/2)x = 1
x = -2/17
Now we can substitute this value of x into the expression we found for y:
y = (-3/2)x - 3
y = (-3/2)(-2/17) - 3
y = 1/17 - 3
y = -50/17
Therefore, the solution to the system is (-2, 1).