Question

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 .Is the statement is true?​

Answer 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 .

$:\implies$ a₁/a₂ = b₁/b₂ = c₁/c₂ = 0

Substitute the value we get

$:\implies$ k/2 = 3/6 = 7/14

$:\implies$ k/2 = 1/2 = 1/2

$:\implies$ k/2 = 1/2 or k/2 = 1/2

$:\implies$ k = 2/2 or k = 2/2

$:\implies$ k = 1 or k = 1

• Hence, the value of k is1 .

So , the given statement is True .

Answer 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