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5x  3y = 8. . . (I)
3x + y = 2 . . . (II)
Multiplying both sides of equation (II) by 3.
9x + 3y = 6 . . . (III)
5x  3y = 8. . . (I)
Now let us add equations (I) and (III)
5x  3y = 8  
+  9x + 3y = 6 
14x = 14 

∴  x = 1 
substituting x = 1 in equation (II)
3x + y = 2
∴ 3×1 + y = 2
∴ 3 + y = 2
∴ y = 1
solution is x = 1, y = 1;
it is also written as (x, y) = (1, 1)