Give All Solutions of the Nonlinear System of Equations, Including $$\begin{array} { c } x ^ { 2 } - x y + y ^ { 2 } = 3 \\2 x ^ { 2 } + x y + 2 y ^ { 2 } = 12\end{array}$$

question 2

Multiple Choice

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
- $$\begin{array} { c } x ^ { 2 } - x y + y ^ { 2 } = 3 \\2 x ^ { 2 } + x y + 2 y ^ { 2 } = 12\end{array}$$

• A) \(\{ ( 1,0 ) , ( - 1,0 ) \}\)
• B) \(\{ ( 2,1 ) , ( 1,2 ) \}\)
• C) \(\{ ( 2,0 ) , ( - 2,0 ) , ( 1,0 ) , ( - 1,0 ) \}\)
• D) \(\{ ( 2,1 ) , ( - 2 , - 1 ) , ( 1,2 ) , ( - 1 , - 2 ) \}\)

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Definitions:

Communist Central Planning

An economic system where the government makes all decisions regarding the production and distribution of goods and services.

Shortages

Situations where the demand for a product or service exceeds the available supply, often leading to waiting lists or increased prices.

Incentive Problem

Refers to situations in which the incentive structures, or rewards and punishments, do not encourage the desired behavior among individuals or entities, leading to efficiency or performance issues.

Communist Central Planning

A system where all economic and production decisions are made by the government, with the aim of equal distribution of wealth.