Verified Answer :

5x+2y=11   x4
4x-3y=18    x5

20x+8y=44
20x-15y=90

23y= -46
y= -46/23 = -2

5x+2*-2=11
5x-4=11
5x=15
x=3

(1) 5x + 2y = 11
(2) 4x - 3y = 18

Multiply (1) by 4 
Multiply (2) by 5

This gives equation (3) and (4) 

(3) 20x + 8y = 44
(4) 20x - 15y = 90

(3) - (4)

23y = -46
 
         -46
 y =  -------- =   -2
          23

Substitute y into equation (2)

4x - 3(-2) = 18
4x + 6 = 18 
4x = 12 
x = 3