Determine the value of k so that the following equation have no solution. 2x+3y=7, 6x- my=24​

1 thought on “Determine the value of k so that the following equation have no solution. 2x+3y=7, 6x- my=24​”

1. 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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