Q

# On comparing the ratios a 1 / a 2 , b 1 / b2 and c 1 / c 2, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident: (ii) 9x + 3y + 12 = 0 18x + 6y + 24 = 0

Q2.    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:

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

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Given, Equations,

$\\9x + 3y + 12 = 0\\ 18x + 6y + 24 = 0$

Comparing these equations with  $a_1x+b_1y+c_1=0\:and\:a_2x+b_2y+c_2=0$, we get

$\\\frac{a_1}{a_2}=\frac{9}{18}=\frac{1}{2},\\\:\frac{b_1}{b_2}=\frac{3}{6}=\frac{1}{2}\:and \\\:\frac{c_1}{c_2}=\frac{12}{24}=\frac{1}{2}$

As we can see

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

It means that both lines are coincident.

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