$\"\"$ \ \

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

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Cramers Rule for three equations containing three variables : \ \

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Consider a system of linear equations as $\"\"$ \ \

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$\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ . \ \

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The solutions of the system are $\"\"$ , $\"\"$ and $\"\"$ . \ \

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Find the determinant $\"\"$ . \ \

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$\"\"$ \ \

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$\"\"$ . \ \

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Find the value of $\"\"$ . \ \

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$\"\"$ \ \

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Since if all the entries in any row or column is equal to $\"\"$ , the value of the determinant is $\"\"$ . \ \

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$\"\"$ . \ \

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Find the value of $\"\"$ . \ \

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$\"\"$ \ \

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$\"\"$ . \ \

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Find the value of $\"\"$ . \ \

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$\"\"$ \ \

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$\"\"$ . \ \

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\ \

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Find the value of $\"\"$ . \ \

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

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$\"\"$ . \ \

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Find the value of $\"\"$ . \ \

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

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$\"\"$ . \ \

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Find the value of $\"\"$ . \ \

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

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$\"\"$ . \ \

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The solution of system of equations is $\"\"$ . \ \

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The solution of system of equations is $\"\"$ .