Use the Gauss-Jordan Method to Solve the System of Equations $$\begin{array}{l}5 x-y+z=8 \\7 x+y+z=6 \\12 x+2 z=14\end{array}$$

question 16

Multiple Choice

Use the Gauss-Jordan method to solve the system of equations.
- $$\begin{array}{l}5 x-y+z=8 \\7 x+y+z=6 \\12 x+2 z=14\end{array}$$

• A) \( \left(\frac{-z+7}{6}, \frac{z-13}{6}, z\right) \)
• B) \( \left(\frac{z+7}{6}, \frac{-z-13}{6}, z\right) \)
• C) \( \left(\frac{-z+7}{6}, \frac{z+13}{6}, z\right) \)
• D) \( \left(\frac{z-7}{6}, \frac{-z-13}{6}, z\right) \)

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Definitions:

Binary Variable

A variable that can take one of two possible values, typically represented as 0 or 1, indicating the absence or presence of some characteristic.

Double-subscripted Variables

Variables represented with two subscripts, often used in mathematical and economic models to denote the elements of matrices or arrays.

Binary Variable

A variable that takes one of two possible values, often used to represent outcomes like success/failure, yes/no, or true/false.

Demand Constraint

A limitation in operations management that affects the maximum demand that can be satisfied given current resources.