Find the Solution or Solutions, If Any Exist, to the System

question 104

Multiple Choice

Find the solution or solutions, if any exist, to the system.
- $$\left\{ \begin{array} { r } x + y + z = 9 \\2 x - 3 y + 4 z = 7\end{array} \right.$$

• A) infinitely many solutions of the form \(x = \frac { 34 } { 5 } + \frac { 7 } { 5 } z , y = - \frac { 11 } { 5 } + \frac { 2 } { 5 } z , z = z\)
• B) infinitely many solutions of the form \(x = \frac { 34 } { 5 } - \frac { 7 } { 5 } z , y = - \frac { 11 } { 5 } + \frac { 2 } { 5 } z , z = z\)
• C) infinitely many solutions of the form \(x = \frac { 34 } { 5 } - \frac { 7 } { 5 } z , y = \frac { 11 } { 5 } + \frac { 2 } { 5 } z , z = z\)
• D) infinitely many solutions of the form \(x = \frac { 34 } { 5 } + \frac { 1 } { 5 } z , y = \frac { 11 } { 5 } + \frac { 2 } { 5 } z , z = z\)

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Definitions:

Government Budget

A financial statement presenting the government's proposed revenues and spending for a fiscal period, reflecting policy priorities and economic goals.

Annually Balanced Budget

A fiscal policy goal where government revenues and expenditures are equal within a one-year period, preventing deficit or surplus.

Great Depression

A major global financial crisis that occurred in the 1930s.

Annual Revenues

The total amount of income generated by a business, government, or organization from its activities over the course of a year before any costs or expenses are deducted.