Question

We have a linear equation 2x + 3y - 8 = 0. Write another linear equation in two variables such that the geometrical representation of the pair so formed is intersecting lines.Now, write two more linear equations so that one forms a pair of parallel lines and the second forms coincident line with the given equation.

Answer 1

Hi ,

Given linear equation is 2x + 3y - 8 = 0

i ) the condition for pair of intersecting

lines is

a1/a2 ≠ b1/b2


Therefore ,

a1/a2 ≠ a2/b2 => 2/3 ≠ a2/b2

a2 ≠ 2k ,

b2 ≠ 3k where k € R.

The required line is 4x + 7y + 5 = 0

ii ) Condition for parallel lines be

a1/a2 = b1/b2 ≠ c1/c2

We can take a1/b1 = a2/b2 = 2/3 and

c1/c2 = -8/2

Therefore ,

The required parallel line be 2x + 3y + 2 = 0

iii ) Condition for co-incident lines is

a1/a2 = b1/b2 = c1/c2

Therefore ,

Required co-incident line is 6x + 9y - 24 = 0

I hope this helps you.

: )