Solve the system of equations by any method. 3x – 4y + 2z = -17 (1) 2x + 4y + z = 21 (2) 2x + 3y + 5z = 28 (3) Enter the exact answer as an ordered triple, (x, Y, z). Hint: There are multiple ways to solve this system of equations. • strategy is to eliminate one of the variables and end up with 2 equations in 2 variables. • One way to do that is to begin with equation 2 to get z = 21 – 2 1 – 4 y. • Then substitute 21 – 2 x – 4 y for z in equations 1 and 3. • You now have 2 equations (the modified equations 1 and 3) in 2 variables (x and y). • Solve this smaller system for a and y and then use z = 21 – 2 x – 4 y to calculate z.
Solve the system of equations by any method. 3x – 4y + 2z = -17 (1) 2x + 4y + z = 21 (2) 2x + 3y + 5z = 28 (3) Enter the exact answer as an ordered triple, (x, Y, z). Hint: There are multiple ways to solve this system of equations. • strategy is to eliminate one of the variables and end up with 2 equations in 2 variables. • One way to do that is to begin with equation 2 to get z = 21 – 2 1 – 4 y. • Then substitute 21 – 2 x – 4 y for z in equations 1 and 3. • You now have 2 equations (the modified equations 1 and 3) in 2 variables (x and y). • Solve this smaller system for a and y and then use z = 21 – 2 x – 4 y to calculate z.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Solving a System of Equations
#### Instructions
Solve the system of equations using any method:
\[
\begin{align}
3x - 4y + 2z &= -17 \quad \quad \quad (1) \\
2x + 4y + z &= 21 \quad \quad \quad (2) \\
2x + 3y + 5z &= 28 \quad \quad \quad (3) \\
\end{align}
\]
Enter the exact answer as an ordered triple, \((x, y, z)\).
#### Hint
There are multiple ways to solve this system of equations:
- **Strategy**: Eliminate one of the variables to end up with 2 equations in 2 variables.
- **Step-by-Step Method**:
1. Begin with Equation (2) to express \( z \) in terms of \( x \) and \( y \):
\[
z = 21 - 2x - 4y.
\]
2. Substitute \( z = 21 - 2x - 4y \) into Equations (1) and (3).
3. This will provide you with two modified equations (from Equations (1) and (3)) with variables \( x \) and \( y \) only.
4. Solve this smaller system for \( x \) and \( y \).
5. Use \( z = 21 - 2x - 4y \) to calculate \( z \).
Good luck solving the system!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F314b57e5-7f54-41b9-a533-cb2fa63c205a%2F7593ad36-d681-4ad5-9864-b86f41cd6e3c%2Fzfchu7f_processed.png&w=3840&q=75)
Transcribed Image Text:### Solving a System of Equations
#### Instructions
Solve the system of equations using any method:
\[
\begin{align}
3x - 4y + 2z &= -17 \quad \quad \quad (1) \\
2x + 4y + z &= 21 \quad \quad \quad (2) \\
2x + 3y + 5z &= 28 \quad \quad \quad (3) \\
\end{align}
\]
Enter the exact answer as an ordered triple, \((x, y, z)\).
#### Hint
There are multiple ways to solve this system of equations:
- **Strategy**: Eliminate one of the variables to end up with 2 equations in 2 variables.
- **Step-by-Step Method**:
1. Begin with Equation (2) to express \( z \) in terms of \( x \) and \( y \):
\[
z = 21 - 2x - 4y.
\]
2. Substitute \( z = 21 - 2x - 4y \) into Equations (1) and (3).
3. This will provide you with two modified equations (from Equations (1) and (3)) with variables \( x \) and \( y \) only.
4. Solve this smaller system for \( x \) and \( y \).
5. Use \( z = 21 - 2x - 4y \) to calculate \( z \).
Good luck solving the system!
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