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

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

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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 to find out k

Now again consider the following relation

So the common solution is 7

Hence for the system of equation have infinitely many solutions

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Similar questions

Find the value of k for which the following pair of linear equations have infinitely many solutions:

$2 x + 3 y = 7, (k - 1) x + (k + 2) y = 3 k .$

k

2 x + 3 y = 7, (k - 1) x + (k + 2) y = 3 k

2 x + 3 y = 4, (k + 2) x + 6 y = 3 k + 2

(k + 1) x + 8 y = 4 k

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

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