Question

Question 6 (iii)
Given the linear equation 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:
coincident lines

Answer 1

Coincident lines
For coincident lines,
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
Hence, the second line can be
6x + 9y - 24 = 0 as
$\frac{a_1}{a_2}=\frac{2}{6}=\frac{1}{3}$
$\frac{b_1}{b_2}=\frac{3}{9}=\frac{1}{3}$ and
$\frac{c_1}{c_2}=\frac{-8}{-24}=\frac{1}{3}$
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$