# Classify the Following Pair of Line as Coincident, Parallel Or Intersecting: 2x + Y − 1 = 0 and 3x + 2y + 5 = 0 - Mathematics

Classify the following pair of line as coincident, parallel or intersecting:

2x + y − 1 = 0 and 3x + 2y + 5 = 0

#### Solution

Let $a_1 x + b_1 y + c_1 = 0 \text { and } a_2 x + b_2 y + c_2 = 0$

(a) The lines intersect if $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$ is true.

(b) The lines are parallel if $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$ is true.

(c) The lines are coincident if $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$ is true.

2x + y − 1 = 0 and 3x + 2y + 5 = 0
Here,
$\frac{2}{3} \neq \frac{1}{2}$
Therefore, the lines 2x + y − 1 = 0 and 3x + 2y + 5 = 0 intersect.
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.1 | Q 6.1 | Page 78