Find the value of k for which each of the following system of equations have infinitely many solutions :

$2 x + 3 y = 2 (k + 2) x + (2 k + 1) y = 2 (k - 1)$

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Solution

GIVEN:

To find: To determine for what value of k the system of equation has infinitely many solutions

We know that the system of equations

For infinitely many solution

Here,

Consider the following for k

Now consider the following

Hence for the system of equation have infinitely many solutions.

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