Question 1 (i)
Do the following pair of linear equations have no solution? Justify your answer.
2x + 4y = 3 and 12y + 6x = 6

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Solution

Condition for no solution $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
2x + 4y = 3 and 12y + 6x = 6
$a_{2} = 6, b_{2} = 12 c_{2} = - 6 \frac{a_{1}}{a_{2}} = \frac{2}{6} = \frac{1}{3}, \frac{b_{1}}{b_{2}} = \frac{4}{12} = \frac{1}{3}, \frac{c_{1}}{c_{2}} = \frac{- 3}{- 6} = \frac{1}{2} \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
Hence, the given pair of linear equations has no solution.

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Question 2 (i)
Do the following equations represent a pair of coincident lines? Justify your answer.
$3 x + \frac{1}{7} y = 3 a n d 7 x + 3 y = 7$

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