Question 1(ii)
Do the following pair of linear equations have no solution? Justify your answer.
x = 2y and y = 2x

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Solution

x = 2y and y = 2x
x – 2y = 0 and 2x – y = 0
$H e r e, a_{1} = 1, b_{1} = - 2, c_{1} = 0 a_{2} = 2, b_{2} = - 1, c_{2} = 0 \frac{a_{1}}{a_{2}} = \frac{1}{2} a n d \frac{b_{1}}{b_{2}} = \frac{2}{1} \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Hence, the given pair of linear equations has unique solution.

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