Find the Complete Solution of the Linear System or Show $$\left\{ \begin{array} { r } x + y + z = 2 \\2 x - 3 y + 2 z = 4 \\4 x + y - 3 z = 1\end{array} \right.$$

question 92

Essay

Find the complete solution of the linear system or show that it is inconsistent. $$\left\{ \begin{array} { r } x + y + z = 2 \\2 x - 3 y + 2 z = 4 \\4 x + y - 3 z = 1\end{array} \right.$$

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Definitions:

Tacit Collusion

An unspoken, implicit agreement among competitors to avoid certain competitive behaviors, such as price undercutting, to stabilize the market and maintain higher prices.

Cartel

An association of independent companies or entities that agree to limit competition between themselves, often to control prices and production in a particular market.

Allocative Efficiency

A state of the economy in which the distribution of resources among different uses is optimal, reflecting consumer preferences and maximizing total societal welfare.

Productive Efficiency

A situation in which a goods or services are produced at the lowest possible cost, utilizing all available resources efficiently.