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  • Solve the following pairs of equations by reducing them to a pair of linear equations: (i) 1 / 2x + 1 by 3y = 2 1 / 3x + 1 / 2y = 13 / 6

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

                (i)    \\\frac{1}{2x} +\frac{1}{3y} = 2\\ \frac{1}{3x} + \frac{1}{2y} = \frac{13}{6}

Answers (1)

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Given Equations,

\\\frac{1}{2x} +\frac{1}{3y} = 2\\ \frac{1}{3x} + \frac{1}{2y} = \frac{13}{6}

Let, 

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

Now, our equation becomes

\frac{p}{2}+\frac{q}{3}=2

\Rightarrow 3p+2q=12........(1)

And

\frac{p}{3}+\frac{q}{2}=\frac{13}{6}

\Rightarrow 2p+3q=13..........(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}{(2)(-13)-(3)(-12)}=\frac{q}{(-12)(2)-(-13)(3)}=\frac{1}{(3)(3)-(2)(2)}

\frac{p}{-26+36}=\frac{q}{-24+39}=\frac{1}{9-4}

\frac{p}{10}=\frac{q}{15}=\frac{1}{5}

p=2,\:and\:q=3

And Hence,

x=\frac{1}{2}\:and\:y=\frac{1}{3}.

Posted by

Pankaj Sanodiya

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