CBSE Class 11-science Answered
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 | 30 Apr, 2014, 08:14: AM
Expert Answer
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 | 30 Apr, 2014, 10:14: AM
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