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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Solution

(i) Given equation are: 5x + 4y + 8 = 0

7x + 6y − 9 = 0

We have And

Thus the pair of linear equation is intersecting.

(ii) Given equation are: 9x + 3y + 12 = 0

18x + 6y + 24 = 0

We have

Thus the pair of linear is coincident lines.

(iii) Given equation are:

We have

Thus the pair of line is parallel lines.

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Similar questions

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 equation intersect at a point, are parallel or coincide:

(i) $5 x - 4 y + 8 = 0$

$7 x + 6 y - 9 = 0$

(ii) $9 x + 3 y + 12 = 0$

$18 x + 6 y + 24 = 0$

(iii) $6 x - 3 y + 10 = 0$

$2 x - y + 9 = 0$

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: