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Byju's Answer
Standard XII
Mathematics
Linear System of Equations
Find the valu...
Question
Find the value of
k
for which each of the following systems of equations have infinitely many solution:
2
x
+
(
k
−
2
)
y
=
k
6
x
+
(
2
k
−
1
)
y
=
2
k
+
5
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Solution
For the system to have infinitely many solutions, lines must coincide each other
⇒
ratio of respective coefficients must be equal (x, y and constant coefficients)
⇒
2
6
=
k
−
2
2
k
−
1
=
k
2
k
+
5
Equate first two equations ;
⇒
2
k
−
1
=
3
k
−
6
⇒
k
=
5
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Q.
Find the values of k for which the following system of equations have infinitely many solutions.
(i) 2x + 3y = 7
(ii) (k + 2)x + (2k + 1)y = 3(2k - 1)
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