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

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.