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  • Solve the following pairs of equations by reducing them to a pair of linear equations: 2 / root x + 3 / root y = 2 4 by root x + 2 / root y = 2

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

                (ii)    \\ \frac{2}{\sqrt x} + \frac{3}{\sqrt y} = 2\\ \frac{4}{\sqrt x} - \frac{9}{\sqrt y} = -1

Answers (1)

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Given Equations,

\\ \frac{2}{\sqrt x} + \frac{3}{\sqrt y} = 2\\ \frac{4}{\sqrt x} - \frac{9}{\sqrt y} = -1

Let, 

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

Now, our equation becomes

2p+3q=2........(1)

And

4p-9q=-1..........(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)(1)-(-9)(-2)}=\frac{q}{(-2)(4)-(1)(2)}=\frac{1}{(2)(-9)-(4)(3)}

\frac{p}{3-18}=\frac{q}{-8-2}=\frac{1}{-18-12}

\frac{p}{-15}=\frac{q}{-10}=\frac{1}{-30}

p=\frac{1}{2},\:and\:q=\frac{1}{3}

So,

p=\frac{1}{2}=\frac{1}{\sqrt{x}}\Rightarrow x=4

q=\frac{1}{3}=\frac{1}{\sqrt{y}}\Rightarrow y=9.

And hence 

x=4\:and\:y=9.

Posted by

Pankaj Sanodiya

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