Solve the System of Equations Using Substitution $$\left\{ \begin{array} { l } y = - x ^ { 2 } + 3 \\x ^ { 2 } + y ^ { 2 } = 5\end{array} \right.$$

question 82

Multiple Choice

Solve the system of equations using substitution.
- $$\left\{ \begin{array} { l } y = - x ^ { 2 } + 3 \\x ^ { 2 } + y ^ { 2 } = 5\end{array} \right.$$

• A) \(x = 1 , y = 4 ; x = 4 , y = 19\)
• B) \(x = 1 , y = 2 ; x = - 1 , y = 2\)
• C) \(x = 2 , y = - 1 ; x = 1 , y = 2 ; x = - 1 , y = 2 ; x = - 2 , y = - 1\)
• D) \(x = 2 , y = - 1 ; x = - 2 , y = - 1\)

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Definitions:

Type II Error

A statistical mistake of failing to reject a false null hypothesis, missing an actual effect or difference when it exists.

Power

In statistics, power refers to the probability that a test will reject a false null hypothesis, essentially measuring the test's capability to detect an effect if there is one.

Body Mass Index

A numerical computation using height and weight to classify an individual's body weight status.

Type I Error

A statistical error that occurs when a null hypothesis is incorrectly rejected when it is actually true.