Solve the System $$\begin{aligned}x - 2 z & = 10 \\3 y + 6 z & = - 27 \\2 x - 2 y & = 6\end{aligned}$$

question 95

Multiple Choice

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent.
- $$\begin{aligned}x - 2 z & = 10 \\3 y + 6 z & = - 27 \\2 x - 2 y & = 6\end{aligned}$$

• A) \(\{ ( 10,0,0 ) \}\)
• B) Infinitely many solutions; dependent
• C) \(\{ ( 2 , - 1 , - 4 ) \}\)
• D) No solution; inconsistent

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Definitions:

SSB

This could refer to several things depending on context; if in statistical analysis, it might not be a standard abbreviation. NO.

SSE

Sum of Squared Errors; a measure used in statistical analysis to quantify the discrepancy between the data and an estimation model.

Sum of Squares Values

A statistical measure that quantifies the total squared deviation of each observation from the mean, used in various analyses like variance calculation.

SSB

Sum of Squares Between groups; a measure used in statistical analysis to quantify the variance among different groups.