https://file.aiquickdraw.com/mathbot/file/1725988030620gvsgtbip.jpg

The system of equations from the image is:

\[
\begin{aligned}
1. &\quad x + 2y + z = 7 \\
2. &\quad x + 3z = 11 \\
3. &\quad 2x - 3y = 1 \\
\end{aligned}
\]

To solve this system using matrices, we'll first express it in matrix form \( AX = B \), where:

\[
A = \begin{bmatrix} 
1 & 2 & 1 \\
1 & 0 & 3 \\
2 & -3 & 0 
\end{bmatrix},
\quad
X = \begin{bmatrix}
x \\
y \\
z 
\end{bmatrix},
\quad
B = \begin{bmatrix}
7 \\
11 \\
1
\end{bmatrix}
\]

Now, I will solve this system using matrix methods.The solution to the system of equations is:

\[
x = 2, \quad y = 1, \quad z = 3
\]

Would you like more details on the method used, or do you have any other questions?

Here are some related questions to expand on this:

1. How does Gaussian elimination work for solving systems of equations?
2. Can this system of equations be solved graphically?
3. What is the determinant of the matrix \( A \) and what does it signify?
4. How can matrix inversion be used to solve this system?
5. How do you solve non-linear systems of equations?

**Tip:** Always check if the determinant of a matrix is non-zero before attempting to solve a system using the inverse method.

Solve the system of equations: x + 2y + z = 7, x + 3z = 11, 2x - 3y = 1

Learn how to solve a system of linear equations using matrix methods. This includes converting the system to matrix form, applying Gaussian elimination, and understanding determinants. Suitable for Grades 10-12.

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