​Solve the System of Linear Equations $$\left\{ \begin{array} { l } 3 x + 6 y = 1 \\6 x + 8 y = 2\end{array} \right.$$

question 26

Multiple Choice

​Solve the system of linear equations $$\left\{ \begin{array} { l } 3 x + 6 y = 1 \\6 x + 8 y = 2\end{array} \right.$$ using the inverse matrix $$\left[ \begin{array} { c c } - \frac { 2 } { 3 } & \frac { 1 } { 2 } \\\frac { 1 } { 2 } & - \frac { 1 } { 4 }\end{array} \right]$$

• A)​ \[\left[ \begin{array} { l }
• x \\
• y
• \end{array} \right] = \left[ \begin{array} { c }
• \frac { 11 } { 12 } \\
• 0
• \end{array} \right]\]
• B)​ \[\left[ \begin{array} { l }
• x \\
• y
• \end{array} \right] = \left[ \begin{array} { l }
• \frac { 1 } { 3 } \\
• 0
• \end{array} \right]\]
• C)​ \[\left[ \begin{array} { l }
• x \\
• y
• \end{array} \right] = \left[ \begin{array} { c }
• \frac { 11 } { 12 } \\\\
• \frac { 1 } { 3 }
• \end{array} \right]\]
• D)​ \[\left[ \begin{array} { l }
• x \\
• y
• \end{array} \right] = \left[ \begin{array} { c }
• \frac { 1 } { 3 } \\
• - \frac { 1 } { 2 }
• \end{array} \right]\]
• E)​ \[\left[ \begin{array} { l }
• x \\
• y
• \end{array} \right] = \left[ \begin{array} { c }
• - \frac { 1 } { 2 } \\
• \frac { 1 } { 3 }
• \end{array} \right]\]

Calculate future consumption or savings outcomes given changes in economic variables such as income, interest rates, and inflation.

Understand and predict the effects of storage and loss on future consumption in resource management scenarios.

Determine the equilibrium interest rate that balances consumption across different periods given a specific utility function.

Understand basic mathematical operations and their applications.

---

Definitions:

Optimization Model

A mathematical model designed to find the best possible solution to a problem within given constraints.

Mathematical Procedures

Systematic operations or calculations that follow a fixed series of steps to solve mathematical problems or analyze data.