Solve the System of Equations $$\left\{ \begin{aligned}- x + y + 2 z & = 0 \\x + 2 y + z & = 6 \\- 2 x - y + z & = - 6\end{aligned} \right.$$

question 195

Multiple Choice

Solve the system of equations.
- $$\left\{ \begin{aligned}- x + y + 2 z & = 0 \\x + 2 y + z & = 6 \\- 2 x - y + z & = - 6\end{aligned} \right.$$

• A) inconsistent (no solution)
• B) \(x = 2 - z\)
• \(y = z + 2\)
• \(z =\) any real number
• C) \(x = z + 2\)
• \(y = 2 - z\)
• \(z =\) any real number
• D) \(x = z + 2\)
• \(y = z - 2\)
• \(z =\) any real number

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Definitions:

Measurement Error

The variation of a number around its true mean due to uncontrolled, essentially random influences; also called error variance.

Random

Characterized by a lack of order, predictability, or specific pattern, often used to describe events or processes.

Sum to Zero

A concept or situation in which the total gain and loss are exactly balanced, resulting in a net effect of zero.

Ambulatory Assessment

A method in psychological research where data on participants' behaviors, physical activities, and experiences are collected in real-time and in naturalistic settings.