Page 24 - 102math-wb-w3-(analytic geometry)_Neat

WORKBOOK

Ex: Are the following pairs of lines parallel?

a) 2x+y = 3 x−2y = 1 b) 4x−2y = −1 2x−y = 2 c) 2x−y = 1 3y−6x = 2

Ex: For which value of k, the following system equation does not have a solution ?
(k−1)x+4y = 1 2x−y = 4

Ex: If the solution set of the following equation system is empty set, find the value of k.
(k+1)x+2y = 1, − 3 (k−2)x+3y = 1

C) Coincident Lines:

If a b c , then the lines and are coincident,
d e f
which means that and are identical lines (same lines).
If and are coincident lines, the system of equations ax+by+c = 0 dx+ey+f =

0
has infinitely many solutions.

Ex: Are the following pairs of lines coincident ? If so, find general form of the solution set of
the system.
a) 4x−2y = 1 2x−y = 2 b) 2x+y = 3 4x+2y−6= 0

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