Give All Solutions of the Nonlinear System of Equations, Including $\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 36 \\x ^ { 2 } - y ^ { 2 } = 36\end{array}$

question 487

Multiple Choice

Give all solutions of the nonlinear system of equations, including those with nonreal complex components.
$\begin{array} { l } x ^ { 2 } + y ^ { 2 } = 36 \\x ^ { 2 } - y ^ { 2 } = 36\end{array}$

• A) {(6,0)}
• B) {(6,0),(-6,0)}
• C) {(0,6),(0,-6)}
• D) {(0,-6)}

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Definitions:

Two-tail Wilcoxon Rank Sum Test

A nonparametric hypothesis test evaluating whether two independent samples come from the same distribution, considering extreme values at both ends.

Two Populations

Refers to comparing or analyzing two distinct groups or datasets in statistical analysis.

Kruskal-Wallis Test

A non-parametric method for testing whether samples originate from the same distribution, used when the ANOVA assumptions cannot be met.

One-tail

Refers to a one-tailed test in statistics where the critical area of a distribution is one-sided so that it tests for the possibility of an effect in one direction.