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

Intersect at a point

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Coincident

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Parallel

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None of these

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Solution

The correct option is A Intersect at a point
The given linear equation are
$\Rightarrow 5 x - 4 y + 8 - 0.... e q 1$

$\Rightarrow a_{1} = 5, b_{1} = - 4, c_{1} = 8$

$\Rightarrow 7 x + 6 y - 9 = 0... e q 2$

$a_{2} = 7, b_{2} = 6, c_{2} = - 9$

$\Rightarrow \frac{a_{1}}{a_{2}} = \frac{5}{7}$

$\Rightarrow \frac{b_{1}}{b_{2}} = \frac{- 4}{6}$

$\Rightarrow \frac{c_{1}}{c_{2}} = \frac{8}{9}$

Comparing

$\Rightarrow \frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}, \frac{c_{1}}{c_{2}}$

$\Rightarrow \frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$

Hence, the line represented by eq1 and eq2 intersect at a point.
Option A is correct.

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Similar questions

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

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