Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically:

(i)


(ii)


(iii)


(iv)


(i) We get,

=


=


=


Hence,


=


Therefore these pair of lines have infinite number of solutions and


x + y = 5


x = 5 - y


putting y = 1,2,3 we get,


x = 5 -1 = 4


x = 5 - 2 = 3


x = 5 - 3 = 2


X



4



3



2



Y



1



2



3



And, 2x + 2y = 10


x =


X



4



3



2



Y



1



2



3



(ii) We get,


=


=


=


Hence,


=


Therefore, these linear equations are parallel to each other and have no possible solution,


Hence,


(iii) We get,


=


=


=


Hence,


=


Therefore, these linear equations are intersecting each other at one point and thus have only one possible solution.


Hence,


=


=


X



0



1



2



Y



6



4



2



And,


=


X



1



2



3



Y



0



2



4



Graphical representation



(iv) We get,


=


=


= s


Hence,


=


Therefore, these linear equations are parallel to each other and have no possible solution,


Hence,


4
1