Question 58529
Without parenthesese we don't know where your fractions begin and end.  If I am misinterpretting this let me know:
L1) {{{x-(5/3)y=7}}}
L2) {{{(4/7)x+y=-13/7}}}
Multiply L1 by 3 and L2 by 7 to clear the fractions.
L1){{{3(x-(5/3)y)=3(7)}}} -->> {{{3x-5y=21}}}
L2){{{7((4/7)x+y)=7(-13/7)}}}-->> {{{4x+7y=-13}}}
Now multiply L1 by 4 and L2 by -3, add L1+L2 to eliminate the x's and solve for y:
L1) {{{4(3x-5y)=4(21)}}} --> {{{12x-20y=84}}}
L2) {{{-3(4x+7y)=-3(-13)}}}--> {{{-12x-21y=39}}}
:
12x-20y=84
-12x-21y=39
____________
-41y=123
{{{-41y/-41=123/-41}}}
{{{y=-3}}} 
Substitute -41/14 in for y in one of the equations and solve for x.
{{{x-(5/3)(-3)=7}}}
{{{x+5=7}}}
{{{x+5-5=7-5}}}
{{{x=2}}}
(x,y)=(2,-3)
Happy Calculating!!!