### Chapter 3: Pair of Linear Equations in Two Variables

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##### Pair of linear equations in two variables CBSE NCERT Solutions

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

Solutions: Let the second line be  $a_2x + b_2y + c_2 = 0$.

Comparing given line 2x + 3y – 8 = 0 with $a_1x + b_1y + c_1 = 0$.

We get  $a_1 = 2 , b_1 = 3 , c_1 = -8$.

Two lines intersect with each other if  $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$ . So, second equation can be x + 2y = 3.

(ii) Let the second line be  $a_2x + b_2y + c_2 = 0$.

Comparing given line 2x + 3y – 8 = 0 with $a_1x + b_1y + c_1 = 0$

We get $a_1 = 2 , b_1 = 3 , c_1 = -8$ .

Two lines are parallel to each other if   $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$.

So, second equation can be 2x + 3y – 2 = 0.

(iii) Let the second line be  $a_2x + b_2y + c_2 = 0$.

Comparing given line 2x + 3y – 8 = 0 with  $a_1x + b_1y + c_1 = 0$.

We get  $a_1 = 2 , b_1 = 3 , c_1 = -8$ .

Two lines are coincident if   $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$  .

So, second equation can be 4x + 6y – 16 = 0.

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