Question

Find the value of k for which the given system of equations has infinitely many solutions kx+2y=k^2., 2x+ky=4

Answer 1

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Answer 2

Answer:

For k = 2, the system of equations will have infinitely many solutions.

Step-by-step explanation:

The given set of equations are

$kx + 2y = k^{2} \\2x + ky = 4$

or, $kx + 2y - k^{2} = 0 \\2x + ky - 4 = 0$

Now, for having infinitely many solutions,

$\frac{k}{2}  = \frac{2}{k}   = \frac{-k^{2} }{-4}$

So, on comparing, we get that K = 2

So, for k = 2, the system of equations will have infinitely many solutions.