Question

For what value of k will the system of linear equations has infinite number of solutions? kx+4y=k-4, 16x+ky=k

Answer 1

★ k=8

★ for further details , refer to the attachment

Answer 2

$\textbf{Answer :}$

Given set of equations is

kx + 4y = k - 4 ...(i)
16x + ky = k ...(ii)

We apply Cramer's rule to find the value of k.

Here,

D = k² - (16 × 4)
= k² - 64
= (k + 8) (k - 8)

D1 = k (k - 4) - 4k
= k² - 4k - 4k
= k² - 8k
= k (k - 8)

D2 = k² - 16 (k - 4)
= k² - 16k + 64
= (k - 8)²
= (k - 8) (k - 8)

For infinite number of solutions, we must have

D = 0 = D1 = D2

⇒ k = 8,
since (k - 8) is the common factor in D, D1 and D2.

∴ the required value of k is 8.

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