Question

Do the following equations represents a pair of coincident line $Rs$ Justify you answer.
$-2x-3y=1$ and $6y+4x=-2$

Answer 1

Condition for coincident lines

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}....\left(i\right)$

here, $\frac{a_1}{a_2}=\frac{-2}{4}=\frac{-1}{2},\frac{b_1}{b_2}=\frac{-3}{6}=\frac{-1}{2}$ and $\frac{c_1}{c_2}=\frac{1}{-2}$

So , the given system of linear equations do satisfy condition (i)