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Solve the following pairs of equations by reducing them to a pair of linear equations: 5 / x - 1 + 1 / y - 2 = 2 6 / x - 1 - 3 / y - 2 = 1

Q1.    Solve the following pairs of equations by reducing them to a pair of linear equations:

                (iv)    \\\frac{5}{x - 1} + \frac{1}{y -2} = 2\\ \frac{6}{x-1} - \frac{3}{y -2} =1

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Given Equations,

\\\frac{5}{x - 1} + \frac{1}{y -2} = 2\\ \frac{6}{x-1} - \frac{3}{y -2} =1

Let, 

\frac{1}{x-1}=p\:and\:\frac{1}{y-2}=q

Now, our equation becomes

5p+q=2........(1)

And

6p-3q=1..........(2)

Multiplying (1) by 3 we get

15p+3q=6..........(3)

Now, adding (2) and (3) we get

21p=7

\Rightarrow p=\frac{1}{3}

Putting this in (2)

6\left ( \frac{1}{3} \right )-3q=1

\Rightarrow 3q=1

\Rightarrow q=\frac{1}{3}

Now,

p=\frac{1}{3}=\frac{1}{x-1}\Rightarrow x-1=3\Rightarrow x=4

q=\frac{1}{3}=\frac{1}{y-2}\Rightarrow y-2=3\Rightarrow x=5

Hence,

x=4,\:and\:y=5. 

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