Question 41432
The steps are simple & easy.. see this
5x/2 - y = 9/10  ..eqn 1
3x/4 + 5y/6 = 2/3..eqn 2

multiply eqn 1 by 10 
you get
25x-10y = 9  ..eqn 3
multiply eqn 2 by 12
9x+10y=8

now it is simple
25x-10y = 9
9x+10y=8
add both 34x=17 (y is eliminated)
x=1/2
then resub this in eqn 3
you get y=7/20

verify
5x/2-y=5/4-7/20=25/20 - 7/20=18/20=9/10
and
3x/4+5y/6=3/8+35/120=45/120+35/120=80/120=8/12=2/3
Cool