Question : 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
Solution : The given linear equation is 2x + 3y – 8 = 0
(i) For intersecting lines, we know that
\(a_1\over a_2\) \(\ne\) \(b_1\over b_2\)
Any intersecting line may be taken as
5x + 2y – 9 = 0
(ii) For parallel lines, \(a_1\over a_2\) = \(b_1\over b_2\) \(\ne\) \(c_1\over c_2\)
\(\therefore\) line parallel to 2x + 3y – 8 = 0 may be taken as
6x + 9y + 7 = 0
(iii) For coincident lines, \(a_1\over a_2\) = \(b_1\over b_2\) = \(c_1\over c_2\)
Any line coincident to 2x + 3y – 8 = 0 may be taken as
4x + 3y – 16 = 0