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, 