Solve the system of equations. X₁ - X₂ + X3 = 8 X₁ + X₂ + X3 = 6 X₁ + X2-X3 = -12 The product of the solution to the system is -18 8 -8 -12
Solve the system of equations. X₁ - X₂ + X3 = 8 X₁ + X₂ + X3 = 6 X₁ + X2-X3 = -12 The product of the solution to the system is -18 8 -8 -12
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![### Solving a System of Equations
Consider the following system of equations:
\[
\begin{align*}
x_1 - x_2 + x_3 &= 8 \\
x_1 + x_2 + x_3 &= 6 \\
x_1 + x_2 - x_3 &= -12
\end{align*}
\]
**Objective:** Determine the product of the solutions to the system.
To find the solution to the given system of linear equations, we need to solve for \( x_1 \), \( x_2 \), and \( x_3 \).
### Multiple Choice Answers:
Please select the correct product of the solutions from the following options:
- \(\bigcirc\) -18
- \(\bigcirc\) 8
- \(\bigcirc\) -8
- \(\bigcirc\) -12
- \(\bigcirc\) 18
- \(\bigcirc\) 6
Proceed by solving the system of equations step by step, substituting and eliminating variables until the values of \( x_1 \), \( x_2 \), and \( x_3 \) are determined. Once the values are found, calculate the product of the three variables and select the corresponding choice.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ecf1484-f95f-4119-9858-43c8382b92c0%2Fd246b701-0a5e-4cb6-9002-311ba8a84840%2Fpozpsf5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving a System of Equations
Consider the following system of equations:
\[
\begin{align*}
x_1 - x_2 + x_3 &= 8 \\
x_1 + x_2 + x_3 &= 6 \\
x_1 + x_2 - x_3 &= -12
\end{align*}
\]
**Objective:** Determine the product of the solutions to the system.
To find the solution to the given system of linear equations, we need to solve for \( x_1 \), \( x_2 \), and \( x_3 \).
### Multiple Choice Answers:
Please select the correct product of the solutions from the following options:
- \(\bigcirc\) -18
- \(\bigcirc\) 8
- \(\bigcirc\) -8
- \(\bigcirc\) -12
- \(\bigcirc\) 18
- \(\bigcirc\) 6
Proceed by solving the system of equations step by step, substituting and eliminating variables until the values of \( x_1 \), \( x_2 \), and \( x_3 \) are determined. Once the values are found, calculate the product of the three variables and select the corresponding choice.
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