Problem: 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.
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.