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

Answer in Brief

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

 2x + y − 1 = 0 and 3x + 2y + 5 = 0

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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.
  Is there an error in this question or solution?
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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
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