Solve the System $$\begin{aligned}4 x + y + z & = 0 \\x - y + 2 z & = - 8 \\4 x + y + z & = - 3\end{aligned}$$

question 58

Multiple Choice

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.
- $$\begin{aligned}4 x + y + z & = 0 \\x - y + 2 z & = - 8 \\4 x + y + z & = - 3\end{aligned}$$

• A) \(\{ ( - 3 , - 1,4 ) \}\)
• B) \(\{ ( - 1,4 , - 3 ) \}\)
• C) \(\varnothing\)
• D) \(\{ ( - 3,4 , - 1 ) \}\)

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Definitions:

Null Hypothesis

A hypothesis that assumes no significant difference or effect in the context of an experiment or test.

Alternative Hypothesis

A hypothesis that contradicts the null hypothesis, suggesting that there is a significant effect or difference.

Test Statistic

A value calculated from sample data during hypothesis testing. It is used to determine whether to reject the null hypothesis.

Alternative Hypothesis

In hypothesis testing, the hypothesis that contradicts the null hypothesis, indicating there is an effect or a difference.