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

First, let's solve one of the equations for one variable in terms of the other variable. Let's solve the first equation for x:

-5x + 2y = 4
-5x = -2y + 4
x = (2y - 4)/5

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

6x - 3y = -7
6((2y - 4)/5) - 3y = -7
(12y - 24)/5 - 3y = -7
12y - 24 - 15y = -35
-3y - 24 = -35
-3y = -11
y = 11/3

Now, substitute this value of y back into the expression for x:

x = (2(11/3) - 4)/5
x = (22/3 - 12/3)/5
x = 10/15
x = 2/3

Therefore, the solution to the system of equations is x = 2/3 and y = 11/3.