Apply Gaussian Elimination to Systems with More Variables Than Equations $$\begin{array} { l } 5 x - y + z = 8 \\7 x + y + z = 6\end{array}$$

question 91

Multiple Choice

Apply Gaussian Elimination to Systems with More Variables than Equations
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
- $$\begin{array} { l } 5 x - y + z = 8 \\7 x + y + z = 6\end{array}$$

• A) \(\left\{ \left( - \frac { 1 } { 6 } z + \frac { 7 } { 6 } , \frac { 1 } { 6 } z - \frac { 13 } { 6 } , z \right) \right\}\)
• B) \(\{ ( - \mathrm { z } + 3,4 \mathrm { z } + 7 , \mathrm { z } ) \}\)
• C) \(\left\{ \left( \frac { 1 } { 6 } z + \frac { 7 } { 6 } , \frac { 1 } { 6 } z , z \right) \right\}\)
• D) \(\varnothing\)

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Definitions:

Long-Run Equilibrium

A state in which supply equals demand, all firms are maximizing profits, and there is no incentive for market entry or exit.

Efficient Output

The level of production at which a firm or economy can produce the maximum amount of goods at the lowest possible cost.

Efficient Output

The level of production where a firm or economy can produce the maximum amount of goods and services with the least amount of inputs.

Perfect Competition

A market structure characterized by a large number of buyers and sellers, homogeneous products, and free entry and exit, leading to price determination by supply and demand.