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# If the lines 3x - 5y + 3 = 0, 5x + 7y - k = 0 and 2x - 3y - 5 = 0 are concurrent, find the value of k.

Asked by Topperlearning User 30th April 2014, 8:14 AM
Lines are said to be concurrent, if they pass through a common point, i.e., point of intersection of any two lines lies on the other line. Here given three lines are
3x - 5y + 3 = 0                                    --- (i)

5x + 7y - k = 0                                   ---(ii)

And 2x - 3y- 5 = 0                             --- (iii)

Solving equation (i) and (iii), we get

x = 34 and y = 21.

Therefore, the point of intersection of two lines (i) and (iii) is (34, 21).
Since above three lines are concurrent, the point (34, 21) will satisfy equation (ii) so that

5 x 34 + 7 x 21- k = 0
170 + 147 - k = 0
k = 317.
Answered by Expert 30th April 2014, 10:14 AM
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