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 in terms of x:

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

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

6x - 3((5/2)x + 2) = -7
6x - (15/2)x - 6 = -7
(12/2)x - (15/2)x = -7 + 6
(-3/2)x = -1
x = 2/3

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

y = (5/2)(2/3) + 2
y = 5/3 + 2
y = 11/3

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