find the values of ‘a’ and ‘b’ if the pair of linear equations (a-4)x +2y+(2b+1)=0 and (a-1)d + 4y +(5b-1)=0 has infinite solution

1 thought on “find the values of ‘a’ and ‘b’ if the pair of linear equations (a-4)x +2y+(2b+1)=0 and (a-1)d + 4y +(5b-1)=0 has infinite solution”

1. Step-by-step explanation:

   2x−(a−4)y=2b+1

   4x−(a−1)y=5b−1

   Considering 2x−(a−4)y=2b+1

   Comparing with

   a

   1

   x+b

   1

   y=c

   1

   a

   1

   =2

   b

   1

   =−(−a−4)

   and c

   1

   =2b+1

   Now considering 4x−(a−1)y=5b−1

   Comparing with

   a

   2

   x+b

   2

   y=c

   2

   a

   2

   =4

   b

   2

   =−(a−1)

   and c

   2

   =5b−1

   For infinite number of solutions ,

   a

   2

   a

   1

   =

   b

   2

   b

   1

   =

   c

   2

   c

   1

   ∴

   4

   2

   =

   −(a−1)

   −(a−4)

   =

   5b−1

   2b+1

   Considering

   a−1

   a−4

   =

   2

   1

   ⇒2a−8=a−1

   ⇒a=7

   And now for b consider

   5b−1

   2b+1

   =

   2

   1

   ⇒4b+2=5b−1

   ∴b=3

   ∴ The given system of equation will have infinitely many solution if a=7 and b=3.

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