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

Answer 2

Answer:

Y = 1/4x-1

X = 4y-1

Step-by-step explanation:

layout the equations :

x+1/y = 4        y+1/x = 1/4

solve the equations, remember to switch sides switch signs solving the equations will give us the value of the letter

x+1/y = 4

x+1 = 4y

x=4y-1

***

y+1/x = 1/4

y+1  = 1/4x

y = 1/4x-1