Question

Question 2 (iii)
Do the following equations represent a pair of coincident lines? Justify your answer.
$\frac{x}{2}+y+\frac{2}{5}=0and4x+8y+\frac{5}{16}=0$

Answer 1

$\frac{x}{2}+y+\frac{2}{5}=0$ and $4x+8y+\frac{5}{16}=0$
Here, $a_1=\frac{1}{2},b_1=1,c_1=\frac{2}{5}$ and
$a_2=4,b_2=8,c_2=\frac{5}{16}$
$\frac{a_1}{a_2}=\frac{\frac{1}{2}}{4}=\frac{1}{8},\frac{b_1}{b_2}=\frac{1}{8}$and
$\frac{c_1}{c_2}=\frac{\frac{2}{5}}{\frac{5}{16}}=\frac{32}{25}$
$\therefore \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
So, the given system of linear equations does not represent a pair of coincident lines.