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

a) Intersecting lines
Solution: For intersecting lines, the linear equations should meet the following condition:
a1/a2 ≠ b1/b2
For getting another equation to meet this criterion, multiply the coefficient of x with any number and multiply the coefficient of y with any other number. A possible equation can be as follows:
4x+9y−8=0
(b) Parallel lines
Solution: For parallel lines, the linear equations should meet the following condition:
a1/a2 = b1/b2 ≠ c1/c2
For getting another equation to meet this criterion, multiply the coefficients of x and y with the same number and multiply the constant term with any other number. A possible equation can be as follows:
4x+6y−24=0
(c) Coincident lines
Solution: For getting coincident lines, the equations should meet the following condition;
a1/a2 = b1/b2 = c1/c2
For getting another equation to meet this criterion, multiply the whole equation with any number. A possible equation can be as follows:
4x+6y−16=0