onsider the three equations of x+ y+ z = 1 and y – x = 0 and y + z = -1. Place them ato a system of equations and then solve that system. Show all work.
onsider the three equations of x+ y+ z = 1 and y – x = 0 and y + z = -1. Place them ato a system of equations and then solve that system. Show all work.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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![**Problem Statement:**
Consider the three equations:
1. \( x + y + z = 1 \)
2. \( y - x = 0 \)
3. \( y + z = -1 \)
Place them into a system of equations and then solve that system. **Show all work.**
**Solution:**
First, we identify the given system of equations:
\[
\begin{align*}
1. & \quad x + y + z = 1 \\
2. & \quad y - x = 0 \\
3. & \quad y + z = -1 \\
\end{align*}
\]
**Step 1: Solve equation 2 for one variable.**
From equation 2:
\[ y - x = 0 \]
\[ y = x \]
**Step 2: Substitute \( y = x \) in equations 1 and 3.**
Substitute into equation 1:
\[ x + x + z = 1 \]
\[ 2x + z = 1 \] \quad (Equation 4)
Substitute into equation 3:
\[ x + z = -1 \] \quad (Equation 5)
**Step 3: Solve the system of equations 4 and 5.**
From equation 5, express \( z \) in terms of \( x \):
\[ z = -1 - x \]
Substitute \( z = -1 - x \) into equation 4:
\[ 2x + (-1 - x) = 1 \]
\[ 2x - x - 1 = 1 \]
\[ x - 1 = 1 \]
\[ x = 2 \]
**Step 4: Find the values of \( y \) and \( z \).**
Since \( y = x \), then:
\[ y = 2 \]
Using the expression for \( z \):
\[ z = -1 - x = -1 - 2 = -3 \]
**Final Solution:**
The solution to the system of equations is:
\[ x = 2, \quad y = 2, \quad z = -3 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea358d9d-257b-44d6-a601-1e462ade83c9%2F3dd88585-fd07-4589-a998-e3e24295797f%2Ftj0x7a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Consider the three equations:
1. \( x + y + z = 1 \)
2. \( y - x = 0 \)
3. \( y + z = -1 \)
Place them into a system of equations and then solve that system. **Show all work.**
**Solution:**
First, we identify the given system of equations:
\[
\begin{align*}
1. & \quad x + y + z = 1 \\
2. & \quad y - x = 0 \\
3. & \quad y + z = -1 \\
\end{align*}
\]
**Step 1: Solve equation 2 for one variable.**
From equation 2:
\[ y - x = 0 \]
\[ y = x \]
**Step 2: Substitute \( y = x \) in equations 1 and 3.**
Substitute into equation 1:
\[ x + x + z = 1 \]
\[ 2x + z = 1 \] \quad (Equation 4)
Substitute into equation 3:
\[ x + z = -1 \] \quad (Equation 5)
**Step 3: Solve the system of equations 4 and 5.**
From equation 5, express \( z \) in terms of \( x \):
\[ z = -1 - x \]
Substitute \( z = -1 - x \) into equation 4:
\[ 2x + (-1 - x) = 1 \]
\[ 2x - x - 1 = 1 \]
\[ x - 1 = 1 \]
\[ x = 2 \]
**Step 4: Find the values of \( y \) and \( z \).**
Since \( y = x \), then:
\[ y = 2 \]
Using the expression for \( z \):
\[ z = -1 - x = -1 - 2 = -3 \]
**Final Solution:**
The solution to the system of equations is:
\[ x = 2, \quad y = 2, \quad z = -3 \]
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