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

Let's use the substitution method.

From the first equation, we can solve for y:
4x - y = -19
y = 4x + 19

Now, we substitute this expression for y into the second equation:
-5x + 7(4x + 19) = 64
-5x + 28x + 133 = 64
23x + 133 = 64
23x = -69
x = -3

Now that we have found the value of x, we can substitute it back into the first equation to find y:
4(-3) - y = -19
-12 - y = -19
y = -19 + 12
y = -7

Therefore, the solution to the system of equations is x = -3 and y = -7.