Question

Question 6 (i)
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:
(i) Intersecting lines

Answer 1

For the lines to be intersecting,
$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

The line given is 2x + 3y - 8 = 0.

$a_1=2$ and $b_1=3$

Hence, the second line can be 2x + 4y - 6 = 0, where $a_2=2$ and $b_2=4$

$\frac{a_1}{a_2}=\frac{2}{2}=1$
$\frac{b_1}{b_2}=\frac{3}{4}$.

Thus,
$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$