2x + 3y-6 = 0 (k+1)x +(2k-1)y-8=0 write #down the condition for no solution Find the value of k.
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Step-by-step explanation:
Consider the given equations.
2x+3y=7
(k−1)x+(k+2)y=3k
The general equations
a
1
x+b
1
y=c
1
a
2
x+b
2
y=c
2
So,
a
1
=2,b
1
=3,c
1
=7
a
2
=k−1,b
2
=k+2,c
2
=3k
We know that the condition of infinite solution
a
2
a
1
=
b
2
b
1
=
c
2
c
1
Therefore,
k−1
2
=
k+2
3
=
3k
7
⇒
k−1
2
=
k+2
3
⇒2k+4=3k−3
⇒k=7
Hence, the value of k is 7.
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