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

For coincident lines,
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

The given line is 2x + 3y - 8 = 0, where $a_1=2$, $b_1=3$ and $c_1=-8$

Hence, the second line can be
6x + 9y - 24 = 0, where $a_2=6$, $b_2=9$ and $c_2=-24$

$\frac{a_1}{a_2}=\frac{2}{6}=\frac{1}{3}$
$\frac{b_1}{b_2}=\frac{3}{9}=\frac{1}{3}$ and
$\frac{c_1}{c_2}=\frac{-8}{-24}=\frac{1}{3}$

Thus, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$