Straight Lines and Pair of Straight Lines

‌2x2+xy−6y2=0
⇒‌‌2x2+4xy−3xy−6y2=0
⇒‌‌2x(x+2y)−3y(x+2y)=0
⇒‌‌(2x−3y)(x+2y)=0
⇒‌‌2x−3y=0‌‌‌⋅⋅⋅⋅⋅⋅⋅(i)
‌ or ‌‌x+2y=0‌‌‌⋅⋅⋅⋅⋅⋅⋅(ii)
Given, x+y−1=0... (iii)
Now on solving Eqs. (i) and (ii) we gel. ( 0,0 ).
On solving Eqs. (ii) and (iii), we get ( 2,−1 ) and solving Eqs. (i) and (iii) we get,
(‌

3

5

,‌

2

5

)
As we observe that, AB≠BC≠AC
Because, AB=√‌

98

25

BC‌=√5
‌ and ‌‌‌AC‌=√‌

13

25