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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Similar questions

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

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Q. Question 3 (i)
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Q. Question 3 (i)
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Consistent Pair of Linear Equations

Standard X Mathematics

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

Condition for no solution a1a2=b1b2≠c1c2 2x + 4y = 3 and 12y + 6x = 6 a2=6,b2=12 c2=−6a1a2=26=13,b1b2=412=13,c1c2=−3−6=12a1a2=b1b2≠c1c2 Hence, the given pair of linear equations has no solution.

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