Question

Compute x/y if

Answer 1

Let first consider the equations one by one and will be solving one by one ;

${:\implies \quad \sf x+\dfrac{1}{y}=4}$

Multiplying both sides by y will lead ;

${:\implies \quad \sf xy+1=4y}$

${:\implies \quad \boxed{\sf xy=4y-1\quad \cdots \cdots(i)}}$

Now, consider the second equation which is ;

${:\implies \quad \sf y+\dfrac{1}{x}=\dfrac14}$

Multiplying both sides by x will yield

${:\implies \quad \sf xy+1=\dfrac{x}{4}}$

${:\implies \quad \sf xy=\dfrac{x}{4}-1}$

${:\implies \quad \boxed{\sf xy=\dfrac{x-4}{4}\quad \cdots \cdots(ii)}}$

As LHS of both equations (i) and (ii) are same, so equating both will yield;

${:\implies \quad \sf 4y-1=\dfrac{x-4}{4}}$

Multiplying both sides by 4 will yield

${:\implies \quad \sf 16y-4=x-4}$

${:\implies \quad \sf 16y=x}$

Dividing both sides by y will yield :

${:\implies \quad \boxed{\bf{\dfrac{x}{y}=16}}}$

Hence, the required answer is 16