Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method.
(i)
Solution:
Comparing equation
with
and
with
, we get
and
and
We have
which means that the two lines are parallel.
Therefore, there is no solution for the given equations.
(ii)
Comparing equation
with
and
with
, we get
and
and
We have
which means that there is unique solution for the given equations.
and
and
(iii)
Comparing
with
and
with
, we get
and
and
We have,
It means lines coincide with each other. Hence, there are infinite many solutions.
(iv)
Comparing
with
and
with
we get,
and
and
We have
which means that we have unique solution for these equations.
and
and
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