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.
