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Byju's Answer
Standard XII
Mathematics
Consistency of Linear System of Equations
For the follo...
Question
For the following system of equation determine the value of k for which the given system of equation has infinitely many solutions.
5
x
+
2
y
=
k
10
x
+
4
y
=
3
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Solution
The given system of equations is
5
x
+
2
y
−
k
=
0
10
x
+
4
y
−
3
=
0
This system of equation 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
=
5
,
b
1
=
2
,
c
1
=
−
k
and
a
2
=
10
,
b
2
=
4
and
c
2
=
−
3
For infinitely many solutions, we must have
a
1
a
2
=
b
1
b
2
=
c
1
c
2
i.e.,
5
10
=
2
4
=
−
k
−
3
⇒
1
2
=
k
3
⇒
k
=
3
2
Hence, the given system of equations will have infinitely many solutions, if
k
=
3
2
.
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Standard XII Mathematics
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