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 :

1. Intersecting lines
2. Parallel lines
3. Coincident lines

Answer 1

1. Given the linear equation are 2x + 3y - 8 = 0

We know that interesting condition

`a_1/a_2 != b_1/b_2`

Where a₁ = 2, b₁ = 3, c₁ = -8

Hence, the equation of other line is x + 2y - 4 = 0

2. We know that parallel line condition is `a_1/a_2 = b_1/b_2≠c_1/c_2`

Where a₁ = 2, b₁ = 3, c₁ = - 8

Hence, the equation is 2x + 6y - 12 = 0

3. We know the coincident line condition is `a_1/a_2 = b_1/b_2 = c_1/c_2`

Where a₁ = 2, b₁ = 3, c₁ = -8

Hence, the equation is 4x + 6y - 16 = 0