Notes

Coincident lines…

$\mathrm{Two\; lines }{a}_{1}x+b_{1}y+c_1=0\mathrm{ and }{a}_{2}x+b_{2}y+c_2=0\mathrm{ are\; said\; to\; be\; coincident\; if\; and\; only\; if}$
$=\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$