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Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Exercise 5
**Exercise #4:**

Solve the system of equations shown below. Show each step in your solution process.

1. \(4x - 2y + 3z = 23\)

2. \(x + 5y - 3z = -37\)

3. \(-2x + y + 4z = 27\)

---

**Note:**
These are challenging problems only because they are long. Be careful and you will be able to solve each of these more complex systems.

---

**Handwritten solution:**

The solved equations and steps are handwritten on the sheet. Key parts of the solution include:

- Combining and manipulating equations to reduce them to a two-by-two system.
- Using substitution or elimination to reduce variables step by step.
- Annotated reduction and simplification of the equations into solvable forms.

The handwritten notes provide transformations and indications of intermediate steps necessary to solve the system, including scalar multiplication of equations and addition or subtraction of equations to eliminate variables.

For more detailed guidance, follow standard procedures to solve linear systems: 

1. Arrange equations systematically.
2. Use elimination or substitution to solve for one variable.
3. Substitute back to find other variables.
4. Check solutions by plugging them back into the original equations.

Practice with these steps will improve problem-solving skills for complex systems.
Transcribed Image Text:**Exercise #4:** Solve the system of equations shown below. Show each step in your solution process. 1. \(4x - 2y + 3z = 23\) 2. \(x + 5y - 3z = -37\) 3. \(-2x + y + 4z = 27\) --- **Note:** These are challenging problems only because they are long. Be careful and you will be able to solve each of these more complex systems. --- **Handwritten solution:** The solved equations and steps are handwritten on the sheet. Key parts of the solution include: - Combining and manipulating equations to reduce them to a two-by-two system. - Using substitution or elimination to reduce variables step by step. - Annotated reduction and simplification of the equations into solvable forms. The handwritten notes provide transformations and indications of intermediate steps necessary to solve the system, including scalar multiplication of equations and addition or subtraction of equations to eliminate variables. For more detailed guidance, follow standard procedures to solve linear systems: 1. Arrange equations systematically. 2. Use elimination or substitution to solve for one variable. 3. Substitute back to find other variables. 4. Check solutions by plugging them back into the original equations. Practice with these steps will improve problem-solving skills for complex systems.
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