Question

x/a - y/b = 0 and ax + by = a2 + b2 . Solve for x and y

Answer 1

x/a - y/b =0 --- 1 , ax + by =a2 + b2 ----2,, x =ya/b substitute in 2,, ya2/b + by = a2 + b2 On LCMon LHS ya2+yb2 / b = a2 + b2 y/b ( a2 + b2 ) = a2 + b2 By cancelling ( a2 + b2) We get [Y=b] and [x= a]

Answer 2

ax2+by=a2+b2………………………..eq2 x/a+y/b=2 or (bx+ay=2ab) …………………..eqI multiplying eq 1 from b and eq ii from a we get b2x +bay=2ab2 …………………..eq3 and a2x –bay=a3-ab2………………..eq4 add both the eq we get x(a2+b2) =ab2(2-1)+a3 x(a2+b2) =ab2(2-1)+a3 then again x(a2+b2) =ab2 +a3 x(a2+b2)=a(a2+b2) x=a