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Find the value(s) of k for which the pair of linear equations

kx+y=k²and x+ky=1 have infinitely many solutions.

User Keona
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1 Answer

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Final answer:

To find the values of k for which the given pair of linear equations have infinitely many solutions, we need to set up the equations and determine the conditions. The value of k can be any real number, meaning there are infinitely many solutions for any value of k.

Step-by-step explanation:

To find the values of k for which the given pair of linear equations have infinitely many solutions, we need to set up the equations and determine the conditions.

Given equations:

kx + y = k² ...(1)

x + ky = 1 ...(2)

To have infinitely many solutions, the two equations must represent the same line. This implies that the slope and y-intercept of the two equations must be the same.

Comparing the equations, we have:

From equation (1): kx + y = k² → y = -kx + k² (3)

From equation (2): x + ky = 1 → x = 1 - ky (4)

Comparing equations (3) and (4), we can see that the slopes of both equations must be the same. Therefore, we have:

-k = -k (5)

From equation (5), we can conclude that the value of k can be any real number. Hence, there are infinitely many solutions for any value of k.

User Nataly Firstova
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