https://file.aiquickdraw.com/mathbot/file/17272166731329qk80nx8.jpg

The system of equations shown in the image is:

\[
\begin{align*}
1. & \quad -6x + 3y - z = 5 \\
2. & \quad 3x - y + 5z = -10 \\
3. & \quad x + 2y + 3z = -1
\end{align*}
\]

To solve this system of linear equations, I will use the elimination or substitution method to find the values of \(x\), \(y\), and \(z\). Let me calculate that for you.

The solution to the system of equations is:

\[
x = \frac{31}{59}, \quad y = \frac{123}{59}, \quad z = \frac{-112}{59}
\]

These are the exact values for \(x\), \(y\), and \(z\).

Would you like to see the steps in detail, or do you have any other questions?

Here are some related questions for deeper understanding:
1. How do we apply the substitution method to solve systems of equations?
2. What is the geometric interpretation of solving a system of three linear equations?
3. Can Gaussian elimination be used to solve this system? How?
4. How do you check if the solution to a system of equations is unique?
5. What happens if the system of equations has no solution or infinitely many solutions?

**Tip:** Always verify the solution by plugging the values of \(x\), \(y\), and \(z\) back into the original equations.

Solve the system of linear equations: -6x + 3y - z = 5, 3x - y + 5z = -10, x + 2y + 3z = -1.

Learn how to solve the system of linear equations -6x + 3y - z = 5, 3x - y + 5z = -10, x + 2y + 3z = -1 using substitution, elimination, or matrix methods. This solution covers key algebraic techniques suitable for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation