Solve the System of Equations $$\left\{ \begin{aligned}2 x - y + 5 z & = - 7 \\x + y - 2 z & = - 2 \\x - y + 4 z & = 8\end{aligned} \right.$$

question 27

Multiple Choice

Solve the system of equations.
- $$\left\{ \begin{aligned}2 x - y + 5 z & = - 7 \\x + y - 2 z & = - 2 \\x - y + 4 z & = 8\end{aligned} \right.$$

• A) \(x = - 3 - z\)
• \(y = 3 z + 1\)
• \(z =\) any real number
• B)
• \[
• \begin{array}{l}
• x=3 z+1 \\
• y=z-3
• \end{array}
• \]
• \( z= \) any real number
• C) \(x = z + 3\)
• \(y = 3 z + 1\)
• \(z =\) any real number
• D) inconsistent (no solution)

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Definitions:

Discount Rate

The interest rate used to discount future cash flows of a financial instrument to their present value, determining the potential investment's value.

Cash Flows

The total amount of money being transferred into and out of a business, indicating its financial health.

Project

A planned endeavor, typically involving research or design, that is carefully planned to achieve a particular aim.

PI

A mathematical constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter; if the context is finance, PI could refer to Profitability Index, indicating the ratio of payoff to investment for a project.