SOLUTION: ax/b-by/a=a+b;ax-by=2ab Please help me solve this equation

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Question 756685: ax/b-by/a=a+b;ax-by=2ab
Please help me solve this equation
Found 2 solutions by Gogonati, dkppathak:
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Assume that a and b are different from zero. Divide both sides of second equation by ab:
%28ax%2Fab%29-%28by%2Fab%29=2
%28x%2Fb%29-%28y%2Fa%29=2 or x%2Fb=2%2B%28y%2Fa%29. Substitute in the first equation the last expression for x%2Fb and get:
a%282%2B%28y%2Fa%29%29-by%2Fa=a%2Bb. Solve the last equation for y and get:
y=-a. Substitute y=-a into x%2Fb=2%2B%28y%2Fa%29and get x=b.
The solution is the point (b,-a)

Answer by dkppathak(439) About Me  (Show Source):
You can put this solution on YOUR website!
ax/b-by/a=a+b (1) by LCM a^2x-b^2y =a^2b+ab^2 (3)
ax-by=2ab (2) by multiplication a a^2x-aby =2a^2b (4) by subtraction equations
-b^2y+aby =-a^2b+ab^2
y(-b^2+ab)=a^2b+ab^2
y= b(a^2+ab)/b(-b+a)
y =a^2+ab/a-b
putting the value of y in eqn (2)

ax-by =2ab
ax-b(a^2+ab)/a-b =2ab
ax=2ab+(a^2b-ab^2)/a-b
ax=2a^2b-2ab^2+a^2b-ab^2/a-b
ax=3a^2b-3ab^2/a-b
ax=3a(ab-b^2)a-b
x=3(ab-b^2)/a-b
ANSWER
x=3(ab-b^2)/a-b
y =a^2+ab/a-b


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