Question 2 (ii)
Do the following equations represent a pair of coincident lines? Justify your answer.
– 2x – 3y = 1 and 6y + 4x = - 2

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Solution

$- 2 x - 3 y = 1$ and $6 y + 4 x = - 2$
Here, $a_{1} = - 2, b_{1} = - 3, c_{1} = - 1$ and
$a_{2} = 4, b_{2} = 6, c_{2} = 2$
$\frac{a_{1}}{a_{2}} = \frac{- 2}{4} = \frac{- 1}{2}, \frac{b_{1}}{b_{2}} = \frac{- 3}{6} = \frac{- 1}{2}$ and $\frac{c_{1}}{c_{2}} = \frac{1}{- 2}$
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
So, the given system of linear equations represent coincident lines.

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Solving Equations Using Method of Substitution

Standard IX Mathematics

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Question 2 (ii) Do the following equations represent a pair of coincident lines? Justify your answer. – 2x – 3y = 1 and 6y + 4x = - 2

−2x−3y=1 and 6y+4x=−2 Here, a1=−2, b1=−3, c1=−1 and a2=4, b2=6, c2=2 a1a2=−24=−12,b1b2=−36=−12 and c1c2=1−2 a1a2=b1b2=c1c2 So, the given system of linear equations represent coincident lines.

Question 2 (ii)
Do the following equations represent a pair of coincident lines? Justify your answer.
– 2x – 3y = 1 and 6y + 4x = - 2