Do the following equations represent a pair of coincident lines? Justify your answer.
$3 x + \frac{1}{7} y = 3$
$7 x + 3 y = 7$

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Solution

We know that the condition for coincident lines,
$a 1 / a 2 = b 1 / b 2 = c 1 / c 2;$
The given pair of linear equations are:
$3 x + \frac{1}{7} y = 3$
$7 x + 3 y = 7$
On comparing the above equations with $a x + b y + c = 0;$
$a_{1} = 3, b_{1} = \frac{1}{7}, c_{1} = - 3;$
$a_{2} = 7, b_{2} = 3, c_{2} = - 7;$
Now, $a 1 / a 2 = 3 / 7$
$b 1 / b 2 = 1 / 21$
$c 1 / c 2 = - 3 / - 7 = 3 / 7$
Here, $a 1 / a 2 \neq b 1 / b 2 .$
Hence, the given pair of linear equations does not represents a pair of coincident lines.

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Question 1(iii)
Do the following pair of linear equations have no solution? Justify your answer.
3x + y – 3 = 0 and 2x + $\frac{2}{3}$ y = 2

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

x + \frac{1}{7} y = 37

x + 3 y = 7

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