College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.1: Systems Of Linear Equations
Problem 83E: Use the system of three equations in three variables to solve each problem. Work schedules A college...
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
Transcribed Image Text:### Solving the System of Equations
Consider the following system of equations:
1. \(2x + 2y + z = -2\)
2. \(-x - 2y + 2z = -5\)
3. \(2x + 4y + z = 0\)
#### Steps to Solve:
1. **Setting Up the Equations**:
- The system consists of three equations with three variables: \(x\), \(y\), and \(z\).
2. **Graph Explanation**:
- A box is shown for the values of \(x\), \(y\), and \(z\), indicating placeholders for the solutions.
- There is a control box with options that might represent actions or adjustments you can make, such as resetting the solution or checking it.
3. **Approach**:
- You can use methods like substitution, elimination, or matrix operations (e.g., Gaussian elimination) to solve the system.
- Regular checks with the given equations ensure that the solutions satisfy all equations.
#### Additional Tools:
- **Interactive Options**: The control box might provide functionalities such as:
- Resetting the problem (\(x\)).
- Information or hints (\(?\)).
- Other tools which appear as icons.
This setup offers an engaging, interactive way to practice solving systems of equations. Utilize any available tools or hints to facilitate finding the solution.
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