Let's use elimination by addition/subtraction:
Mult. the 2nd eqn by 2, obtaining x/2 + 4y/3 = 10. Now subtract the first eqn from this result:
x/2 + 4y/3 = 10
-(X/2+ y/3 = 4
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3y/3 = 6, or y = 2.
Now subst. 2 for y in either of the original equations and solve the result for x:
x/4 + 2(2)/3 = 5 Mult all 3 terms by 12 to eliminate the fractions:
3x + 16 = 60 => 3x = 44, and so x = 44/3.
The solution is (44/3, 2).
