Question 2 (iii)
On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.
6x – 3y + 10 = 0
2x – y + 9 = 0

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Solution

6x – 3y + 10 = 0
2x – y + 9 = 0

Comparing these equations with $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ , we get,
$a_{1} = 6, b_{1} = - 3, a n d c_{1} = 10$
$a_{2} = 2, b_{2} = - 1 a n d c_{2} = 9$

$\frac{a_{1}}{a_{2}} = \frac{6}{- 3} = - \frac{2}{1}$

$\frac{b_{1}}{b_{2}} = \frac{2}{- 1} = - \frac{2}{1}$ and

$\frac{c_{1}}{c_{2}} = \frac{10}{9}$

Hence, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

Therefore, the lines representing the given pair of linear equations are parallel

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Question 2 (i)
On comparing the ratios $\frac{a_{1}}{a_{2}}$ , $\frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.
5x - 4y + 8 = 0
7x + 6y - 9 = 0

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$ , and without drawing them, find out whether the lines representing the following pairs of linear equation intersect at a point, are parallel or coincide: