Do the following pair of linear equations have no solution? Justify your answer.
$ x=2 y $
$ y=2 x $

Given :

The given pair of equations is,

\( x=2 y \)

\( y=2 x \)

To find :

We have to find whether the given pair of equations has no solution.

Solution:

We know that,

The condition for no solution is

$\frac{a_1}{a_2}=\frac{b_1}{b_2}≠\frac{c_1}{c_2}$

\( x-2 y=0 \)

\( 2 x-y=0 \)

Here,

$a_1=1, b_1=-2, c_1=0$

$a_2=2, b_2=-1, c_2=0$

Therefore,

$\frac{a_1}{a_2}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{-2}{-1}=2$

$\frac{c_1}{c_2}=\frac{-3}{-6}=\frac{1}{2}$

Here,

$\frac{a_1}{a_2}≠\frac{b_1}{b_2}$

Hence, the given pair of linear equations has a unique solution.

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Updated on: 10-Oct-2022

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