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Standard IX

Mathematics

Applications of Pair of Equations

Question 2 ii...

Question

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

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Solution

9x + 3y + 12 = 0
18x + 6y + 24 = 0
Comparing these equations with,
$a_{1} x + b_{1} y + c_{1} = 0$
$a_{2} x + b_{2} y + c_{2} = 0$
We get,
$a_{1} = 9, b_{1} = 3, a n d c_{1} = 12$
$a_{2} = 18, b_{2} = 6 a n d c_{2} = 24$
$\frac{a_{1}}{a_{2}} = \frac{9}{18} = \frac{1}{2}$
$\frac{b_{1}}{b_{2}} = \frac{3}{6} = \frac{1}{2}$ and
$\frac{c_{1}}{c_{2}} = \frac{12}{24} = \frac{1}{2}$
Hence, $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$
Therefore, both lines are coincident.

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Q. On comparing the ratios

\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}

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$18 x + 6 y + 24 = 0$

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

$2 x - y + 9 = 0$

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Question 2 (ii) On comparing the ratios a1a2 , b1b2 and c1c2 , 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

9x + 3y + 12 = 0 18x + 6y + 24 = 0 Comparing these equations with, a1x+b1y+c1=0 a2x+b2y+c2=0 We get, a1=9,b1=3, and c1=12 a2=18,b2=6 and c2=24 a1a2=918=12 b1b2=36=12 and c1c2=1224=12 Hence, a1a2=b1b2=c1c2 Therefore, both lines are coincident.

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