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

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

2x + 3y – 8 = 0

The condition for intersecting lines is 

So we multiply any value with a1  and not with b1

If we multiply by 2  second such equation  will

4x + 3y – 8 = 0

(i)              parallel lines

the condition for parallel lines is 

So multiply with a1 , b1 with any number and not multiply with c

if we multiply by 2 then second equation will

4x + 6y – 8 = 0

(ii)            coincident lines

the condition for coincident lines are

So multiply by any number with whole equation

                         If we multiply by 2 we get

4x +  6y – 16 = 0