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,
$a_{1} x + b_{1} y + c_{1} = 0$
$a_{2} x + b_{2} y + c_{2} = 0$
We get,
$a_{1} = 6, b_{1} = - 3, a n d c_{1} = 10$
$a_{2} = 2, b_{2} = - 1 a n d c_{2} = 9$
$\frac{a_{1}}{a_{2}} = \frac{6}{2}, \frac{3}{1}$
$\frac{b_{1}}{b_{2}} = \frac{- 3}{- 1} = \frac{3}{1}$ and
$\frac{c_{1}}{c_{2}} = \frac{12}{24} = \frac{1}{2}$
Hence, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
Therefore, both lines 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

Q. 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 :
(i)

5 x - 4 y + 8 = 0

7 x + 6 y - 9 = 0

(ii)

9 x + 3 y + 12 = 0

18 x + 6 y + 24 = 0

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Question 2 (iii) On comparing the ratios a1a2, b1b2 and c1c2 , 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

6x – 3y + 10 = 0 2x – y + 9 = 0 Comparing these equations with, a1x+b1y+c1=0 a2x+b2y+c2=0 We get, a1=6,b1=−3, and c1=10 a2=2,b2=−1 and c2=9 a1a2=62,31 b1b2=−3−1=31 and c1c2=1224=12 Hence, a1a2=b1b2≠c1c2 Therefore, both lines are parallel.

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