Question

Question 2 (ii)
Do the following equations represent a pair of coincident lines? Justify your answer.
– 2x – 3y = 1 and 6y + 4x = - 2

Answer 1

$-2x-3y=1$ and $6y+4x=-2$
Here, $a_1=-2,b_1=-3,c_1=-1$ and
$a_2=4,b_2=6,c_2=2$
$\frac{a_1}{a_2}=\frac{-2}{4}=\frac{-1}{2},\frac{b_1}{b_2}=\frac{-3}{6}=\frac{-1}{2}$ and $\frac{c_1}{c_2}=\frac{1}{-2}$
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
So, the given system of linear equations represent coincident lines.