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  • Solve the following pairs of equations by reducing them to a pair of linear equations: (v) 7x - 2y / xy = 5 8x + 7y / xy = 15

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

                (v)    \\\frac{7x - 2y}{xy} = 5\\ \frac{8x + 7y}{xy} = 15

Answers (1)

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Given Equations,

\\\frac{7x - 2y}{xy} = 5\\\\\Rightarrow\frac{7}{y} -\frac{2}{x}=5\\ \frac{8x + 7y}{xy} = 15\\\Rightarrow \frac{8}{y}+\frac{7}{x}=15

Let, 

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

Now, our equation becomes

7q-2p=5........(1)

And

8q+7p=15..........(2)

By Cross Multiplication method,

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

\frac{q}{(-2)(-15)-(7)(-5)}=\frac{p}{(-5)(8)-(-15)(7)}=\frac{1}{(7)(7)-(8)(-2)}

\frac{q}{30+35}=\frac{p}{-40+105}=\frac{1}{49 +16}

\frac{q}{65}=\frac{p}{65}=\frac{1}{65}

p=1,\:and\:q=1

And Hence,

x=1\:and\:y=1.

Posted by

Pankaj Sanodiya

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