Question

solve the simultaneous equation 41/x-47/y=35; 47/x-41/y =53

Answer 1

Let's make it easier, add both of them you get $\frac{1}{x} + \frac{1}{y} = 1$ and subtract one from other, $\frac{1}{x} - \frac{1}{y} = 3$. Now you get x=1/2 and y=-1.

Answer 2

Sol:-
           41/x-47/y=35  (eq1)
           47/x-41/y=53  (eq2)
  Now add eq1 &eq2, we get
     41(1/x-1/y)+47(1/x-1/y) = 83
 =>(41+47)(1/x-1/y)=83
 =>1/x-1/y=1
 =>1/x=1+1/y (eq3)
Therefore by eq3 in eq1 we get x=1/2 & y=1