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.
$6 x - 3 y + 10 = 0; 2 x - y + 9 = 0$

Intersect at a point

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Parallel

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Coincident

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Data insufficient

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Solution

The correct option is B Parallel
The given linear equation are
$\Rightarrow 6 x - 3 y + 10 = 0.... e q 1$
$\Rightarrow a_{1} = 6, b_{1} = - 3, c_{1} = 10$
$\Rightarrow 2 x - y + 9 = 0... e q 2$
$\Rightarrow a_{2} = 2, b_{2} = - 1, c_{2} = 9$
$\Rightarrow \frac{a_{1}}{a_{2}} = \frac{6}{3} \Rightarrow= \frac{3}{1}$
$\Rightarrow \frac{b_{1}}{b_{2}} = \frac{- 3}{- 1}$
$\Rightarrow \frac{c_{1}}{c_{2}} = \frac{10}{9}$
comparing
$\Rightarrow \frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}, \frac{c_{1}}{c_{2}}$
$\Rightarrow \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
Hence,the line represented by eq1 and eq2 are parallel.

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Similar questions

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

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, or are parallel or coincident.

9 x + 3 y + 12 = 0; 18 x + 6 y + 24 = 0

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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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

The correct option is B ParallelThe given linear equation are⇒6x−3y+10=0....eq1⇒a1=6,b1=−3,c1=10⇒2x−y+9=0...eq2⇒a2=2,b2=−1,c2=9⇒a1a2=63⇒=31⇒b1b2=−3−1⇒c1c2=109comparing⇒a1a2,b1b2,c1c2⇒a1a2=b1b2≠c1c2Hence,the line represented by eq1 and eq2 are parallel.

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.
$6 x - 3 y + 10 = 0; 2 x - y + 9 = 0$