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Solve the following pairs of equations by reducing them to a pair of linear equations:4 / x + 3y =- 14 3 / x - 4y = 23

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

                (iii)    \\\frac{4}{x} + 3y = 14\\ \frac{3}{x} - 4y = 23

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Given Equations,

\\\frac{4}{x} + 3y = 14\\ \frac{3}{x} - 4y = 23

Let, 

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

Now, our equation becomes

\Rightarrow 4p+3q=14........(1)

And

\Rightarrow 3p-4q=23..........(2)

By Cross Multiplication method,

\frac{p}{b_1c_2-b_2c_1}=\frac{q}{c_1a_2-c_2a_1}=\frac{1}{a_1b_2-a_2b_1}

\frac{p}{(3)(-23)-(-4)(-14)}=\frac{q}{(-14)(3)-(-23)(4)}=\frac{1}{(4)(-4)-(3)(3)}

\frac{p}{-69-56}=\frac{q}{-42+92}=\frac{1}{-16-9}

\frac{p}{-125}=\frac{q}{50}=-\frac{1}{25}

p=5,\:and\:q=-2

And Hence,

x=\frac{1}{5}\:and\:y=-2.

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