Solve x/b+y/a=2 x/a+y/b=a²+b²/ab

Question

x/b+y/a= 2
x/a+y/b= a²+b²/ab

The answer is one of the following choices:

A) X= -B Y= A

B) X= B Y= -A

C) X= B/2 Y= 2A

D) X= -B Y= -2A

E) None of the above.

Answer 1

ax+by=2ab from the first equation.

by=2ab-ax,

y=2a-(ax/b).

x/a+y/b=x/a+2a/b-ax/b²=(a²+b²)/ab=a/b+b/a,

x(1/a-a/b²)=b/a-a/b=(b²-a²)/ab,

x(b²-a²)/ab²=(b²-a²)/ab,

x=ab²/ab=b.

Therefore y=2a-ab/b=2a-a=a. So x=b, y=a (answer E).

CHECK

x/b+y/a=1+1=2✔️

x/a+y/b=b/a+a/b=(a²+b²)/ab✔️