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 pair of linear equations intersect at a point, are parallel or coincident:
$a x - b y = - 1; b x + a y = - 1$
where $a \neq 0, b \neq 0$

Coincident

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Parallel

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Intersect at a point

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None of these

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Solution

The correct option is C Intersect at a point
The given pair of linear equations is
$a x - b y + 1 = 0; b x + a y + 1 = 0$
Here $a_{1} = a, b_{1} = - b, c_{1} = 1$
and $a_{2} = b, b_{2} = a, c_{2} = 1$
$∴ \frac{a_{1}}{a_{2}} = \frac{a}{b}, \frac{b_{1}}{b_{2}} = \frac{- b}{a}, \frac{c_{1}}{c_{2}} = \frac{1}{1}$
Hence $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Thus the lines represented by given pair of linear equation can be intersect at a point.

Suggest Corrections

Similar questions

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.
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

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