Write the system of linear equations that is represented by the given augmented matrix. Assume that the variables are x1 and x2.
[3 6 | 2]
[1 4 | 9]

The augmented matrix given is:

\[
\begin{bmatrix}
3 & 6 & | & 2 \\
1 & 4 & | & 9 \\
\end{bmatrix}
\]

This represents a system of linear equations where the first row corresponds to the coefficients of \(x_1\) and \(x_2\) in the first equation, and the second row corresponds to the coefficients of \(x_1\) and \(x_2\) in the second equation.

The system of linear equations is:

\[
3x_1 + 6x_2 = 2
\]
\[
x_1 + 4x_2 = 9
\]

Would you like more details or clarification on any step?

Here are 5 related questions for further practice:
1. How would you solve this system of equations using substitution?
2. How would you solve this system using the elimination method?
3. How would you convert this system into row-echelon form?
4. What would the solution be if you graphed these equations?
5. How would you represent this system of equations in matrix form?

**Tip**: To solve systems of equations efficiently, try row reduction to simplify the augmented matrix and find the solution step by step!

Write the system of linear equations that is represented by the given augmented matrix. Assume that the variables are x1 and x2. [3 6 | 2] [1 4 | 9]

Learn how to write and solve a system of linear equations represented by the augmented matrix [3 6 | 2], [1 4 | 9]. This problem explores linear algebra concepts such as matrices and systems of equations, suitable for high school students in Grades 9-12.

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