Compute x/y if

x + 1/y = 4 and

y + 1/x = 1/4

Please explain the process on how to solve it- I’ll give brainliest!


  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

  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
    y+1/x = 1/4
    y+1  = 1/4x
    y = 1/4x-1


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