On comparing the ratios a_1 a_2 , b_1 b_2 and c_1 c_2 , and witho… - Vidyadip

Question

On comparing the ratios $\frac{\text{a}_1}{\text{a}_2},\frac{\text{b}_1}{\text{b}_2}$ and $\frac{\text{c}_1}{\text{c}_2},$ and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide.

$9x + 3y + 12 = 0$

$18x + 6y + 24 = 0$

✓

Answer

Given equation are:
$9x + 3y + 12 = 0$
$18x + 6y + 24 = 0$
Where, $a_1 = 9, b_1 = 3, c_1= 12$
$a_2 = 18, b_2 = 6, c_3= 24$
We get $\frac{\text{a}_1}{\text{a}_2}=\frac{9}{18},\frac{\text{b}_1}{\text{b}_2}=\frac{3}{6}$
and $\frac{\text{c}_1}{\text{c}_2}=\frac{12}{24}$
$\Rightarrow\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}=\frac{\text{c}_1}{\text{c}_2}=\frac{1}{2}$
Thus the pair of linear equation are coincide.

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