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Solve the following pairs of equations by reducing them to a pair of linear equations: (vIii) Pair of Linear Equations in Two Variables Exercise 3.6 1

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

                    (viii)    \\\frac{1}{3x + y} + \frac{1}{3x -y} = \frac{3}{4}\\ \frac{1}{2(3x+y)} - \frac{1}{2(3x -y)} = \frac{-1}{8}

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Given Equations,

\\\frac{1}{3x + y} + \frac{1}{3x -y} = \frac{3}{4}\\ \frac{1}{2(3x+y)} - \frac{1}{2(3x -y)} = \frac{-1}{8}

Let, 

\frac{1}{3x+y}=p\:and\:\frac{1}{3x-y}=q

Now, our equation becomes

p+q=\frac{3}{4}.........(1)

And

\\\frac{p}{2}-\frac{q}{2}=\frac{-1}{8}\\\\p-q=\frac{-1}{4}..........(2)

Now, Adding (1) and (2), we get

2p=\frac{3}{4}-\frac{1}{4}

\Rightarrow 2p=\frac{2}{4}

\Rightarrow p=\frac{1}{4}

Putting this value in (1)

\frac{1}{4}+q=\frac{3}{4}

\Rightarrow q=\frac{3}{4}-\frac{1}{4}

\Rightarrow q=\frac{2}{4}

\Rightarrow q=\frac{1}{2}

Now,

p=\frac{1}{4}=\frac{1}{3x+y}

\Rightarrow 3x+y=4...........(3)

And

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

\Rightarrow 3x-y=2............(4)

Now, Adding (3) and (4), we get

6x=4+2

\Rightarrow 6x=6

\Rightarrow x=1

Putting this value in (3),

3(1)+y=4

\Rightarrow y=4-3

\Rightarrow y=1

Hence,

x=1,\:and\:y=1

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