Do the following pair of linear equations have no solution? Justify your answer.
$2 x + 4 y = 3$ and $10 y + 5 x = 6$

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Solution

Condition for no solution $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
$2 x + 4 y = 3$ and $10 y + 5 x = 6$
$a_{1} = 2, b_{1} = 4, c_{1} = - 3 a_{2} = 5, b_{2} = 10, c_{2} = - 6 \frac{a_{1}}{a_{2}} = \frac{2}{5}, \frac{b_{1}}{b_{2}} = \frac{4}{10} = \frac{2}{5}, \frac{c_{1}}{c_{2}} = \frac{- 3}{- 6} = \frac{1}{2} \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
Hence, the given pair of linear equations has no solution.

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Do the following pair of linear equations have no solution? Justify your answer. 2x+4y=3 and 10y+5x=6

Condition for no solution a1a2=b1b2≠c1c2 2x+4y=3 and 10y+5x=6 a1=2,b1=4,c1=−3a2=5,b2=10,c2=−6a1a2=25,b1b2=410=25,c1c2=−3−6=12a1a2=b1b2≠c1c2 Hence, the given pair of linear equations has no solution.

Do the following pair of linear equations have no solution? Justify your answer.
$2 x + 4 y = 3$ and $10 y + 5 x = 6$