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

(i) intersecting lines

(ii) parallel lines

(iii) coincident lines

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#### Solution

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

We know that interesting condition

`a_1/a_2 != b_1/b_2`

Where `a_1 = 2, b_1 = 3, c_1 = -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`

Where `a_1 = 2, b_1 = 3, c_1 = - 8

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

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

Where `a_1 = 2, b_1 = 3, c= -8`

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

Concept: Graphical Method of Solution of a Pair of Linear Equations

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