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Byju's Answer
Standard X
Mathematics
Inconsistent Pair of Linear Equations
Find the valu...
Question
Find the value of
k
for which the given simultaneous equations have infinitely many solutions:
4
x
+
y
=
7
,
16
x
+
k
y
=
28
.
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Solution
4
x
+
y
=
7
and
16
x
+
k
y
=
28
Comparing the above equation with the equation
a
1
x
+
b
1
y
=
c
1
and
a
2
x
+
b
2
y
=
c
2
respectively.
a
1
=
4
,
b
1
=
1
,
c
1
=
7
,
a
2
=
16
,
b
2
=
k
,
c
2
=
28
Apply the condition for infinitely many solution.
a
1
a
2
=
4
16
=
1
4
,
b
1
b
2
=
1
k
and
c
1
c
2
=
1
4
∴
The condition for the simultaneous equations to have infinitely many solutions is.
a
1
a
2
=
b
1
b
2
=
c
1
c
2
∴
1
4
=
1
k
=
1
4
∴
1
4
=
1
k
∴
k
=
4
.
Hence the simultaneous equations
4
x
+
y
=
7
and
16
x
+
k
y
=
28
will have infinitely many solutions for
k
=
4
.
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Q.
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Q.
Find the value(s) of
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