For the given pair of equation kx+3y= -7
and 2x+6y= -14 to have infinitely many solution ,
the value of k should be 1 .I

2 thoughts on “For the given pair of equation kx+3y= -7<br />and 2x+6y= -14 to have infinitely many solution ,<br />the value of k should be 1 .I”

1. Answer

   • 1st equation = kx + 3y +7 = 0

   • 2nd equation = 2x + 6y +14 = 0

   a₁ = k ,b₁ = 3 , c₁ = 7

   a₂ = 2 , b₂ = 6 ,c₂ = 14

   ⠀⠀⠀⠀⠀⠀⠀⠀⠀According to the Question

   it is given that the given pair of equation has infinitely many solution . So , the condition for infinitely many solution .

   [tex]:\implies[/tex] a₁/a₂ = b₁/b₂ = c₁/c₂ = 0

   Substitute the value we get

   [tex]:\implies[/tex] k/2 = 3/6 = 7/14

   [tex]:\implies[/tex] k/2 = 1/2 = 1/2

   [tex]:\implies[/tex] k/2 = 1/2 or k/2 = 1/2

   [tex]:\implies[/tex] k = 2/2 or k = 2/2

   [tex]:\implies[/tex] k = 1 or k = 1

   • Hence, the value of k is1 .

   So , the given statement is True .

   Reply

2. Answer:

   Given :–

   For the given pair of equation kx+3y= -7

   and 2x+6y= -14 to have infinitely many solution

   To Find :–

   Value of k

   Solution :–

   We know that

   a1/a2 = b1/b2 = c1/c2

   k/2 = 3/6 = 7/14

   k/2 = 1/2 = 7/14

   k/2 = 1/2 = 1/2

   k × 2/2 × 1 = 1/2

   2k/2 = 1/2

   2k = 2

   k = 1

   [tex] \\ [/tex]

   Reply