On comparing the ratios
and
, find out whether the following pair of linear equations are consistent, or inconsistent.
(i)
Comparing equation
with
and
with
, we get
and
and
which means equations have unique solution.
Hence they are consistent.
(ii)
Comparing equation
with
and
with
, we get
and
We have
because
Therefore, equations have no solution because they are parallel.
Hence, they are inconsistent.
(iii)
Comparing equation
with
and
with
, we get
and
We have
So,
Therefore, equations have unique solution. Hence, they are consistent
(iv)
Comparing equation
with
and
with
, we get
and
and
We have
The lines have infinite many solutions. Hence, they are consistent.
(v)
Comparing equation
with
and
with
, we get
and
and
We have
.
Therefore, lines have infinite many solutions. It means that they are consistent
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