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Let's first rewrite the system of equations as:

\[
x - 3y = 0
\]
\[
-1 + 3y = -4x
\]

To form the augmented matrix, we need both equations in standard form: \( ax + by = c \).

For the first equation:
\[
x - 3y = 0 \quad \text{(already in standard form)}
\]

For the second equation, rearrange it as:
\[
-4x + 3y = 1
\]

Now, we can form the augmented matrix. The augmented matrix represents the coefficients of \( x \) and \( y \) on the left side and the constants on the right side.

\[
\begin{pmatrix}
1 & -3 & 0 \\
-4 & 3 & 1
\end{pmatrix}
\]

This is the augmented matrix for the given system of equations.

Would you like any more details on how the matrix was formed, or do you have any further questions?

Here are some related questions for practice:
1. How do you solve a system of equations using the augmented matrix method?
2. What are the properties of matrices that can be helpful in solving linear equations?
3. How do you perform row reduction to solve an augmented matrix?
4. Can every system of linear equations be represented by an augmented matrix?
5. What is the significance of the determinant in matrix operations?

**Tip:** When writing the augmented matrix, always ensure the equations are in standard form (\( ax + by = c \)) for easier matrix construction.

Write the augmented matrix for the following system of equations:
x - 3y = 0
-1 + 3y = -4x

Learn how to write the augmented matrix for the system of linear equations x - 3y = 0 and -1 + 3y = -4x. This problem covers essential concepts in linear algebra, including converting systems into matrix form. Suitable for high school students in Grades 9-12.

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