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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Solution

For lines to be coincident,

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

The given pair of linear equations are:

$3 x + \frac{y}{7} - 3 = 0$

and 7x + 3y – 7 = 0

$w h e r e a_{1} = 3, b_{1} = \frac{1}{7}, c_{1} = - 3 a_{2} = 7, b_{2} = 3, c_{2} = - 7 n o w, \frac{a_{1}}{a_{2}} = \frac{3}{7}, \frac{b_{1}}{b_{2}} = \frac{1}{21}, \frac{c_{1}}{c_{2}} = \frac{3}{7}$

Here, $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

Thus, the given pair of equations does not represent coincident lines.

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

x + 3 y = 7

\frac{x}{2} + y + \frac{2}{5} = 0 a n d 4 x + 8 y + \frac{5}{16} = 0

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

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