To solve this system of equations, we can use the method of substitution or elimination.

Let's solve for y in the first equation:

x - 3y + 8 = 0
3y = x + 8
y = (1/3)x + 8/3

Now we can substitute this expression for y into the second equation:

3x - 4((1/3)x + 8/3) - 3 = 0
3x - (4/3)x - 32/3 - 3 = 0
9x - 4x - 32 - 9 = 0
5x - 41 = 0
5x = 41
x = 41/5
x = 8.2

Now we can plug this value of x back into the first equation to find y:

y = (1/3)(8.2) + 8/3
y = 2.733 + 2.6667
y = 5.3997

Therefore, the solution to the system of equations is x = 8.2 and y = 5.3997.