On comparing the ratios
and
find out whether the following pair of linearequations are consistent, or inconsistent.
(i) ![]()
(ii) ![]()
(iii) ![]()
(iv) ![]()
(v) ![]()
(i) We get,
= ![]()
=![]()
= ![]()
Hence,
= ![]()
Therefore , these linear equations will intersect at one point only and have only one possible solution.
And, ![]()
(ii) We get,
= ![]()
=![]()
= ![]()
Hence,
=![]()
Therefore, these linear equations are parallel to each other and have no possible solution.
And, ![]()
(iii) ![]()
9x – 10y = 14
We get,
= ![]()
=![]()
= ![]()
Hence,
= ![]()
Therefore, these linear equations will intersect each other at one point and have only one possible solution.
And, pair of linear equations is consistent.
(iv) We get,
= ![]()
=![]()
= ![]()
Hence,
= ![]()
Therefore these pair of lines have infinite number of solutions. and ![]()
v) We get,
= ![]()
=![]()
= ![]()
Hence,
= ![]()
Therefore these pair of lines have infinite number of solutions and pair of linear equation is consistent.