https://file.aiquickdraw.com/mathbot/file/1726456093896yfq2ni4u.jpg

The augmented matrix in the image is:

\[
\begin{bmatrix}
1 & 0 & 0 & -5 \\
0 & 1 & 0 & -1 \\
0 & 0 & 1 & -3 \\
\end{bmatrix}
\]

This matrix represents a system of equations in row-reduced echelon form, where each row corresponds to an equation for a variable. From this matrix, we can deduce the solution to the system:

- The first row corresponds to \( x = -5 \)
- The second row corresponds to \( y = -1 \)
- The third row corresponds to \( z = -3 \)

Thus, the solution to the system of equations is:
\[
x = -5, \quad y = -1, \quad z = -3
\]

Let me know if you would like more details or have any questions! Here are five related questions:

1. How do you perform row reduction on a matrix to reach this form?
2. What is the significance of the augmented matrix in solving systems of equations?
3. Can every system of equations be written as an augmented matrix?
4. What happens if one row in the matrix contains all zeros?
5. How can you tell if a system of equations has no solution or infinitely many solutions from the matrix?

**Tip:** To solve systems of equations using matrices, always aim to convert the matrix into row-reduced echelon form for direct solutions.

A system of equations was written as an augmented matrix, which was row reduced to: 
[1 0 0 -5]
[0 1 0 -1]
[0 0 1 -3]. What is the solution to the original system of equations?

Discover how to solve a system of equations using an augmented matrix reduced to row-reduced echelon form (RREF). In this example, the solution to the system is x = -5, y = -1, and z = -3. Perfect for students in Grades 9-12 exploring linear algebra concepts.

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