determine the value of k for which the following system of linear equations has infinitely of solutions (k-3)X + 3 Y=K K X + K Y =12determine the value of k for which the following system of linear equations has infinitely of solutions (k-3)X + 3 Y=K K X + K Y =12
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9th
Maths
Linear Equations in Two Variable
Solution of Linear Equations in Two Variables
Find the value of k for whi...
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Asked on November 22, 2019 by
Dhanaswi Gorain
Find the value of k for which the system of equations
kx−y=2
6x−2y=3
has no solution. Is there a value of k for which the system has infinitely many solution?
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ANSWER
Given
kx−y=2
6x−2y=3
kx−y−2=0
6x−2y−3=0
We know that for a
1
x+b
1
y+c
1
=0,a
2
x+b
2
y+c
2
=90
a
2
a
1
=
b
2
b
1
=
c
2
c
1
⇒ for no solution
a
1
=k,b=−1,c
1
=−2
a
2
=b,b
2
=−1,c
2
=−3
6
k
=
−2
−1
=
−3
−2
⇒
6
k
=
2
1
=
3
2
for no solution
6
k
=
2
1
nd
2
1
=
3
2
⇒k=
2
6
⇒
k=3
for infinite solution
b
1
a
1
=
b
2
b
1
=
c
2
c
1
b
k
=
−2
−1
=
−3
−2
+2
+1
=
−3
+2
=
2
1
=
3
2
Here is no value of k the system has infinite solution.