Question

if the equation 5x + ky =3 and kx + 5y = 3 represent the same line then k=?

Answer 1

Answer:

k = 5

Step-by-step explanation:

 we have a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0

 so a1 = 5, b1 = k , c1 = -3

     a2 = k, b2 = 5, c2 = -3

a1/a2 = b1/b2 or 5/k = k/5

   k^2 = 25 or k = 5

b1/b2 = k/5 = 5/5 = 1

c1/c2 = -3/-3 = 1

Now a1/a2 = b1/b2 = c1/c2 = 1

hence k =5

Answer 2

Answer:

k = 5

Step-by-step explanation:

Write 5x + ky = 3 in the y = mx + c format:

5x + ky = 3

ky = -5x + 3

y = -5/kx + 3/k

Write 5x + ky = 3 in the y = mx + c format:

kx + 5y = 3

5y = -kx + 3

y = -k/5x + 3/5

Comparing y = -5/kx + 3/k and y = -k/5x + 3/5

⇒ k = 5

Answer: k = 5