Solve the System by the Method of Substitution $$\left\{ \begin{array} { l } x ^ { 2 } + y = 1 \\x + y = - 15\end{array} \right.$$

question 27

Multiple Choice

Solve the system by the method of substitution. $$\left\{ \begin{array} { l } x ^ { 2 } + y = 1 \\x + y = - 15\end{array} \right.$$

• A) \(\left( \frac { 1 - \sqrt { 65 } } { 2 } , \frac { - 31 - \sqrt { 65 } } { 2 } \right) , \left( \frac { 1 + \sqrt { 65 } } { 2 } , \frac { - 31 + \sqrt { 65 } } { 2 } \right)\)
• B) \(\left( \frac { 1 - \sqrt { 65 } } { 2 } , \frac { - 31 + \sqrt { 65 } } { 2 } \right) , \left( \frac { 1 + \sqrt { 65 } } { 2 } , \frac { - 31 - \sqrt { 65 } } { 2 } \right)\)
• C) \(\left( \frac { - 1 + \sqrt { 59 } } { 2 } , \frac { - 29 + \sqrt { 65 } } { 2 } \right) , \left( \frac { - 1 + \sqrt { 59 } } { 2 } , \frac { - 29 - \sqrt { 65 } } { 2 } \right)\)
• D) \(\left( \frac { 1 - \sqrt { 59 } } { 2 } , \frac { - 29 + \sqrt { 65 } } { 2 } \right) , \left( \frac { 1 - \sqrt { 59 } } { 2 } , \frac { - 29 - \sqrt { 65 } } { 2 } \right)\)
• E)no solution exists

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Definitions:

Edgeworth Box

A diagram used in economics to show the distribution of resources and the allocation of goods in a two-person, two-good economy.

Contract Curve

In economics, the curve that represents the set of Pareto efficient allocations in an Edgeworth Box diagram.

Utility Function

A symbolic depiction illustrating the ranking of preferences a consumer holds across various goods or outcomes.

Edgeworth Box

A diagram used in economics to show the distribution of resources and the potential gains from trade between two individuals in a pure exchange economy.