Question

3x3x-5y-7=0 X=2k-1. Y=k

Answer 1

Answer:

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.