Q. If the lines and are concurrent, then the value of is

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Solution:

Three 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 third line. Here given lines are
(i)
(ii)
(iii)
Solving Eqs. (i) and (iii) by cross-multiplication method, we get

Therefore, the point of intersection of two lines is . Since, above three lines are concurrent, the point will satisfy Eq. (ii), so that