x/5-y/4=15/10 ··· Eq.1, x/2-y/3=5/6 ···Eq.2 Multiply both sides of Eq.1 by 20, and Eq.2 by 6, getting
4x-5y=30 ··· Eq.3, 3x-2y=5 ··· Eq.4 Multiply both sides of Eq.3 by 2, and Eq.4 by 5, getting
8x-10y=60 ··· Eq.5, 15x-10y=25 ··· Eq.6 From Eq.5, we have:
10y=8x-60 Substitute this into Eq.6, getting
15x-(8x-60)=25 Remove the brackets, 15x-8x+60=25, so 7x=-35 Divide both sides by 7.
We have: x=-5 Substitute x=-5 into Eq.3, 4(-5)-5y=30, so -5y=50 Divide both sides by -5.
We have: y=-10
The answer is: x=-5 and y=-10