Q. 64.0( 5 Votes )
Classify the following pairs of lines as coincident, parallel or intersecting:
(i) 2x + y – 1 = 0 and 3x + 2y + 5 = 0
(ii) x – y = 0 and 3x – 3y + 5 = 0
(iii) 3x + 2y – 4 = 0 and 6x + 4y – 8 = 0
Answer :
Let a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 be the two lines.
(a) The lines intersect if 
is true.
(b) The lines are parallel if 
is true.
(c) The lines are coincident if 
is true.
(i) Given: 2x + y − 1 = 0 and 3x + 2y + 5 = 0
Explanation:
Here, 
Therefore, the lines 2x + y − 1 = 0 and 3x + 2y + 5 = 0 intersect.
(ii) Given: x − y = 0 and 3x − 3y + 5 = 0
Explanation:
Here, 
Therefore, the lines x − y = 0 and 3x − 3y + 5 = 0 are parallel.
(iii) Given: 3x + 2y − 4 = 0 and 6x + 4y − 8 = 0
Explanation:
Here, 
Therefore, the lines 3x + 2y − 4 = 0 and 6x + 4y − 8 = 0 are coincident.
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