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Use Cramer's Rule to Solve (If Possible) the System of Equations

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Use Cramer's Rule to solve (if possible) the system of equations.
{5x4y+z=12x+2y2z=123x+y+z=2\left\{ \begin{array} { r } 5 x - 4 y + z = - 12 \\- x + 2 y - 2 z = 12 \\3 x + y + z = - 2\end{array} \right.


Definitions:

Pure Competition

A market structure characterized by a large number of small firms, a homogeneous product, perfect information, and easy entry and exit from the market.

Monopoly

A market structure characterized by a single seller offering a unique product or service, with significant barriers to entry for potential competitors.

Price

The financial requisition expected, imposed, or presented for something.

Output

The total amount of products or services produced by a company or economy in a given period.

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