Find out whether the lines representing the following pairs of linear equation intersect at a point, are parallel or coincident: $5 x - 4 y + 8 = 0$ and $7 x + 6 y - 9 = 0$

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Solution

$\frac{a_{1}}{a_{2}} = \frac{5}{7}$
$\frac{b_{1}}{b_{2}} = \frac{- 4}{6} = \frac{- 2}{3}$
Since $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Therefore given pair of lines intersect at a point

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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.

5 x - 4 y + 8 = 0; 7 x + 6 y - 9 = 0

Q. 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

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}}

, and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide :

(i) 5x − 4y + 8 = 0
7x + 6y − 9 = 0

(ii) 9x + 3y + 12 = 0
18x + 6y + 24 = 0

(iii) 6x − 3y + 10 = 0
2x − y + 9 = 0

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Find out whether the lines representing the following pairs of linear equation intersect at a point, are parallel or coincident: 5x−4y+8=0 and 7x+6y−9=0

a1a2=57b1b2=−46=−23Since a1a2≠b1b2Therefore given pair of lines intersect at a point

Find out whether the lines representing the following pairs of linear equation intersect at a point, are parallel or coincident: $5 x - 4 y + 8 = 0$ and $7 x + 6 y - 9 = 0$

$\frac{a_{1}}{a_{2}} = \frac{5}{7}$
$\frac{b_{1}}{b_{2}} = \frac{- 4}{6} = \frac{- 2}{3}$
Since $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Therefore given pair of lines intersect at a point