By comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}, \frac{c_{1}}{c_{2}}$ , find out whether the pairs of linear equations intersect at a point, are parallel find :
$9 x + 3 y + 12 = 0 18 x + 6 y + 24 = 0$

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Solution

We have,
9x + 3y + 12 = 0

18x + 6y – 24 = 0

Here, a1 = 9, b2 = 3, c1 = 12

a1 = 18, b2 = 6, c1 = -24

∴

∴ Both the lines will coincide.

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Question 2 (ii)
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.
9x + 3y + 12 = 0
18x + 6y + 24 = 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

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

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

$2 x - y + 9 = 0$

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.

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

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By comparing the ratios a1a2,b1b2,c1c2, find out whether the pairs of linear equations intersect at a point, are parallel find :9x+3y+12=018x+6y+24=0

We have,9x + 3y + 12 = 018x + 6y – 24 = 0Here, a1 = 9, b2 = 3, c1 = 12a1 = 18, b2 = 6, c1 = -24∴ ∴ Both the lines will coincide.

By comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}, \frac{c_{1}}{c_{2}}$ , find out whether the pairs of linear equations intersect at a point, are parallel find :
$9 x + 3 y + 12 = 0 18 x + 6 y + 24 = 0$

We have,
9x + 3y + 12 = 0

18x + 6y – 24 = 0

Here, a1 = 9, b2 = 3, c1 = 12

a1 = 18, b2 = 6, c1 = -24

∴

∴ Both the lines will coincide.