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

First, solve one of the equations for one of the variables. Let's solve the first equation for y:

4x - y = 9
y = 4x - 9

Now, substitute this expression for y into the second equation:

3x - 7(4x - 9) = -1
3x - 28x + 63 = -1
-25x + 63 = -1
-25x = -64
x = 64/25

Now that we have found the value of x, we can substitute it back into the first equation to find y:

y = 4(64/25) - 9
y = 256/25 - 9
y = 256/25 - 225/25
y = 31/25

Therefore, the solution to the system of equations is x = 64/25 and y = 31/25.