Write the System of Linear Equations Represented by the Augmented $\left[ \begin{array} { l l l : l } 1 & 2 & 1 & - 5 \\0 & 1 & 2 & - 6 \\0 & 0 & 1 & - 1\end{array} \right]$

question 24

Multiple Choice

Write the system of linear equations represented by the augmented matrix. Then use back-substitution to find the solution. Use variables x , y , and z . $\left[ \begin{array} { l l l : l } 1 & 2 & 1 & - 5 \\0 & 1 & 2 & - 6 \\0 & 0 & 1 & - 1\end{array} \right]$

• A) \(\left\{ \begin{array} { r }
• x + 2 y + z = - 5 \\
• y + 2 z = - 6 \\
• z = - 1
• \end{array} \right.\)
• \(( - 4,4 , - 1 )\)
• B) \(\left\{ \begin{array} { r }
• x + 2 y + z = - 5 \\
• y + 2 z = - 6 \\
• z = - 1
• \end{array} \right.\)
• \(( - 4,4 , - 1 )\)
• C) \(\left\{ \begin{array} { r }
• x + 2 y + z = - 5 \\
• y + 2 z = - 6 \\
• z = - 1
• \end{array} \right.\)
• \(( 4,4 , - 1 )\)
• D) \(\left\{ \begin{array} { r }
• x + 2 y + 2 z = - 5 \\
• y + z = - 6 \\
• z = - 1
• \end{array} \right.\)
• \(( 4,4 , - 1 )\)
• E) \(\left\{ \begin{array} { r }
• x + 2 y + z = - 5 \\
• y + 2 z = - 6 \\
• z = - 1
• \end{array} \right.\)
• \(( 4 , - 4 , - 1 )\)

Understand and apply the concept of break-even analysis and leverage, including the calculation and significance of the degree of operating leverage.

Analyze the impact of changes in sales volume, costs (fixed and variable), and price on profit.

Calculate and interpret the margin of safety and its significance in business decision-making.

Apply critical thinking to assess the impact of pricing decisions on net income and break-even points.

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