Question

If the systems of equations (k-3)x+3y=2k and 2x + (k-4)y=8 has infinity many solutions then the value of k is

(a) 1 only
(b) 6 only
(c) 1 and 6
(d) 5 only
​

Answer 1

Step-by-step explanation:

We know that the system of equations

a

1

x+b

1

y=c

1

a

2

x+b

2

y=c

2

has infinitely many solutions, if

a

2

a

1

=

b

2

b

1

=

c

2

c

1

Here, a

1

=2,b

1

=3,c

1

=4,a

2

=k+2,b

2

=6,c

2

=3k+2.

Therefore, the given system of equations will have infinitely many solutions, if

k+2

2

=

6

3

=

3k+2

4

⇒

k+2

2

=

6

3

and

6

3

=

3k+2

4

⇒

k+2

2

=

2

1

and

2

1

=

3k+2

4

⇒k+2=4 and 3k+2=8

⇒k=2 and k=2

⇒k=2

Hence, the given system of equations will have infinitely many solutions, if k=2.

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