Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Educational Website Content: Solving Systems of Equations**
---
### Solve the following system of equations:
\[
\begin{cases}
(1) \quad x - y + 3z = 15 \\
(2) \quad -y + z = 6 \\
(3) \quad z = 1 \\
\end{cases}
\]
* Note: Students can enter a maximum of 2000 characters for their answers.
**Instructions:**
To solve this system of equations, follow these steps:
1. **Start with Equation (3):**
\[ z = 1 \]
This value of \( z \) can now be substituted into the other equations.
2. **Substitute \( z = 1 \) into Equation (2):**
\[ -y + 1 = 6 \]
\[ -y = 5 \]
\[ y = -5 \]
3. **Substitute \( y = -5 \) and \( z = 1 \) into Equation (1):**
\[ x - (-5) + 3(1) = 15 \]
\[ x + 5 + 3 = 15 \]
\[ x + 8 = 15 \]
\[ x = 7 \]
So the solution to the system of equations is:
\[ x = 7, \quad y = -5, \quad z = 1 \]
**Please enter your detailed solution below:**
```
[Text Entry Box]
```
---
**Note:** Make sure to verify each step to ensure accuracy. You can enter your detailed steps and final answer in the text box provided. If you have any questions, feel free to ask for clarification!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf6f4faa-bb31-4351-9b90-23a290e16aec%2F0cebe2e7-83ce-4b12-8262-5b8f3d6dce06%2Fmpwfv4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content: Solving Systems of Equations**
---
### Solve the following system of equations:
\[
\begin{cases}
(1) \quad x - y + 3z = 15 \\
(2) \quad -y + z = 6 \\
(3) \quad z = 1 \\
\end{cases}
\]
* Note: Students can enter a maximum of 2000 characters for their answers.
**Instructions:**
To solve this system of equations, follow these steps:
1. **Start with Equation (3):**
\[ z = 1 \]
This value of \( z \) can now be substituted into the other equations.
2. **Substitute \( z = 1 \) into Equation (2):**
\[ -y + 1 = 6 \]
\[ -y = 5 \]
\[ y = -5 \]
3. **Substitute \( y = -5 \) and \( z = 1 \) into Equation (1):**
\[ x - (-5) + 3(1) = 15 \]
\[ x + 5 + 3 = 15 \]
\[ x + 8 = 15 \]
\[ x = 7 \]
So the solution to the system of equations is:
\[ x = 7, \quad y = -5, \quad z = 1 \]
**Please enter your detailed solution below:**
```
[Text Entry Box]
```
---
**Note:** Make sure to verify each step to ensure accuracy. You can enter your detailed steps and final answer in the text box provided. If you have any questions, feel free to ask for clarification!
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