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The system of equations is

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$\"\"$

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Definition of augment matrix :

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If $\"\"$ are the system of equations then the augmented matrix is $\"\"$ .

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Augment matrix of the system of equations is

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$\"\"$

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Apply $\"\"$ .

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$\"\"$

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Apply $\"\"$ .

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$\"\"$

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Apply $\"\"$ .

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$\"\"$

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Number of variables $\"\"$ .

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Rank of the Matrix $\"\"$ is 3.

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Rank of the augmented matrix $\"\"$ is 2.

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Rank of $\"\"$ < Rank of $\"\"$ , the system has infinitely many solutions.

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Solutions of system of equations are

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$\"\"$

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$\"\"$

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Consider $\"\"$ , then

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$\"\"$

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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The solutions of system of equations are $\"\"$ .

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Infinitely many solutions.

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The solutions of system of equations are $\"\"$ .