the following system of equations determine whether the system has unique solution no solution or infinitely many solution in each case if there is a unique solution find it.
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In the following system of equation determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it.
−3x+4y=5
2
9
x−6y+
2
15
=0.
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ANSWER
The given system of equations may be written as
−3x+4y−5=0
2
9
x−6y+
2
15
=0
The given system of equations is of the form
a
1
x+b
1
y+c
1
=0
a
2
x+b
2
y+c
2
=0
where, a
1
=−3,b
1
=4,c
1
=−5 and a
2
=
2
9
,b
2
=−6,c
2
=
2
15
We have,
a
2
a
1
=
9/2
−3
=
3
−2
,
b
2
b
1
=
−6
4
=
3
−2
and
c
2
c
1
=
15/2
−5
=
3
−2
Clearly,
a
2
a
1
=
b
2
b
1
=
c
2
c
1
So, the given system of equations has infinitely many solutions.
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