Given the linear equation (2x + 3y – 8 = 0), write another linear equation in two variables

(i) Let the second line be equal to a₂x + b₂y + c₂ = 0,

Intersecting Lines:For this Condition,

The Second line such that it is intersecting the given line is
2x+4y-6=0 As,

(ii) Let the second line be equal to a₂x + b₂y + c₂ = 0,

parallel Lines:
For this Condition,

Hence,the second line can be 4x+6y-8=0

(iii) Let the second line be equal to a₂x + b₂y + c₂ = 0,

Coincident lines: For coincident lines,

Hence,the second line can be 6x+9y-24=0

As,