Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables such that the geometrical representation of pair formed is:

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

Answer 1

Solution: (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

(ii)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

(iii) 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