*solve*
5x+2y = 16
-4x+3y = -2

Two equations are given in the quastion and there are two unknown variables "x" and "y" in them. So solving will not be an issue at all.
Taking the first equation:
5x + 2y = 16
2y = 16 - 5x
y = 8 - (5x/2)
Now putting the value of x found from the first equation in the second equation, we get
-4x + 3y = -2
-4x + 3(8 - 5x/2) = -2
-4x + 24 - 15x/2 = -2
-8x + 48 -15x = -4
-23x = -4 - 48
-23x = -52
x = 52/23
Now putting the value of x in the first equation we get
5x + 2y = 16
5(52/23) + 2y = 16
260/23 + 2y = 16
260 + 46y = 368
46y = 368 - 260
46y = 108
y = 108/46
   = 54/23
So the value of x is 52/23 and the value of y is 54/23