https://file.aiquickdraw.com/mathbot/file/17281894820581rkt6dgx.jpg

The system of equations presented in the image is:

\[
\begin{cases}
2y + 7 = -9x \\
-11 + x = 6y
\end{cases}
\]

To write this system as a single matrix equation, we first need to arrange the equations into a standard linear form of \( Ax = b \), where:

- \( A \) is the coefficient matrix,
- \( x \) is the column vector of variables,
- \( b \) is the constants column vector.

### Step 1: Rearranging the equations

Rearrange both equations to isolate the variables \(x\) and \(y\) on the left-hand side:

1. \( 9x + 2y = -7 \)
2. \( x - 6y = 11 \)

### Step 2: Write the system in matrix form

We can now express this system as:

\[
\begin{pmatrix}
9 & 2 \\
1 & -6
\end{pmatrix}
\begin{pmatrix}
x \\
y
\end{pmatrix}
=
\begin{pmatrix}
-7 \\
11
\end{pmatrix}
\]

### Conclusion:

The matrix equation is:

\[
\begin{pmatrix}
9 & 2 \\
1 & -6
\end{pmatrix}
\begin{pmatrix}
x \\
y
\end{pmatrix}
=
\begin{pmatrix}
-7 \\
11
\end{pmatrix}
\]

Let me know if you need more details or further clarifications.

---

Here are 5 related questions to expand your understanding:

1. How do you solve a system of equations using matrix inversion?
2. What is the determinant of a 2x2 matrix, and how is it used in solving systems of equations?
3. How does Gaussian elimination work in solving matrix equations?
4. What is the significance of linear independence in a system of equations?
5. How can systems of equations be solved graphically?

**Tip**: Always check if the determinant of a matrix is non-zero before attempting to find its inverse. If the determinant is zero, the system does not have a unique solution.

Write the following system of equations as a single matrix equation: 2y + 7 = -9x and -11 + x = 6y.

Learn how to express a system of linear equations as a matrix equation. This problem covers key concepts in linear algebra, including matrix representation of variables and coefficients, and is suitable for Grades 10-12 or college students.

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