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 

(ii) parallel lines 

(iii) coincident lines

(i) To find another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines, it should satisfy below condition;

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

For,  2x + 3y – 8 = 0, $a_1= 2 , b_1=3$

Thus, another equation could be 3x + 7y + 9 = 0, such that;

$\frac{a_1}{a_2}=\frac{2}{3},\frac{b_1}{b_2}=\frac{3}{7}$.