Question

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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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?

MEDIUM

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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.