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✔️