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: (iii) 6x - 3y + 10 = 0 2x - y + 9 = 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:

(iii)    $\\6x - 3y + 10 = 0\\ 2x - y+ 9 = 0$

Views

Give, Equations,

$\\6x - 3y + 10 = 0\\ 2x - y+ 9 = 0$

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

$\frac{a_1}{a_2}=\frac{6}{2}=3,\:\frac{b_1}{b_2}=\frac{-3}{-1}=3\:and\:\frac{c_1}{c_2}=\frac{10}{9}$

As we can see

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

It means that both lines are parallel to each other.

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