This is a Test of Mathematics Solution Subjective 63 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.

If any one pair among the straight lines ax + by = a + b, bx –(a + b)y = – a, (a + b)x –ay = b intersect, then show that the three straight lines are concurrent.

Solution:

Three lines are concurrent if each of them is linear combination of other two & they are not parallel. Now given one pair intersect that is they are not parallel. Now ax + by = a + b … (i) bx – (a + b)y = – a …(ii) (a +b)x –ay = b …(iii) (i) + (ii) – (iii) = 0 So they are concurrent.