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The problem asks you to determine the values of \( x \) and \( y \) from matrix equations. Let's go through each part one by one.

### Part a:
\[
\begin{pmatrix} x \\ 5 \end{pmatrix} = \begin{pmatrix} 7 \\ 2y \end{pmatrix} + \begin{pmatrix} -1 \\ -11 \end{pmatrix}
\]

First, let's simplify the right-hand side:
\[
\begin{pmatrix} 7 \\ 2y \end{pmatrix} + \begin{pmatrix} -1 \\ -11 \end{pmatrix} = \begin{pmatrix} 7 - 1 \\ 2y - 11 \end{pmatrix} = \begin{pmatrix} 6 \\ 2y - 11 \end{pmatrix}
\]

Now we have:
\[
\begin{pmatrix} x \\ 5 \end{pmatrix} = \begin{pmatrix} 6 \\ 2y - 11 \end{pmatrix}
\]

By comparing elements of the vectors:
1. \( x = 6 \)
2. \( 5 = 2y - 11 \)

Solving for \( y \) in the second equation:
\[
5 + 11 = 2y \implies 16 = 2y \implies y = 8
\]

Thus, for part (a), the solution is:
\[
x = 6, \quad y = 8
\]

---

### Part b:
\[
\begin{pmatrix} 9 \\ 2y \end{pmatrix} + \begin{pmatrix} -6 \\ -y \end{pmatrix} = \begin{pmatrix} 3 \\ y \end{pmatrix}
\]

First, simplify the left-hand side:
\[
\begin{pmatrix} 9 \\ 2y \end{pmatrix} + \begin{pmatrix} -6 \\ -y \end{pmatrix} = \begin{pmatrix} 9 - 6 \\ 2y - y \end{pmatrix} = \begin{pmatrix} 3 \\ y \end{pmatrix}
\]

Now we have:
\[
\begin{pmatrix} 3 \\ y \end{pmatrix} = \begin{pmatrix} 3 \\ y \end{pmatrix}
\]

This is an identity, meaning that part (b) holds for any value of \( y \). Therefore, **\( y \) is undetermined**, and any \( y \) satisfies the equation.

---

### Part c:
\[
\begin{pmatrix} 2x \\ 2y \end{pmatrix} + \begin{pmatrix} 3y \\ 3x \end{pmatrix} = \begin{pmatrix} 11 \\ 4 \end{pmatrix}
\]

First, simplify the left-hand side:
\[
\begin{pmatrix} 2x \\ 2y \end{pmatrix} + \begin{pmatrix} 3y \\ 3x \end{pmatrix} = \begin{pmatrix} 2x + 3y \\ 2y + 3x \end{pmatrix}
\]

Now we have the equation:
\[
\begin{pmatrix} 2x + 3y \\ 2y + 3x \end{pmatrix} = \begin{pmatrix} 11 \\ 4 \end{pmatrix}
\]

By comparing elements of the vectors:
1. \( 2x + 3y = 11 \)
2. \( 2y + 3x = 4 \)

Now we have a system of two equations:
\[
2x + 3y = 11 \quad \text{(Equation 1)}
\]
\[
2y + 3x = 4 \quad \text{(Equation 2)}
\]

Let me solve this system.

I'll subtract Equation 1 from Equation 2:
\[
(2y + 3x) - (2x + 3y) = 4 - 11
\]
\[
2y + 3x - 2x - 3y = -7
\]
\[
(x - y) = -7
\]
Thus:
\[
x = y - 7 \quad \text{(Equation 3)}
\]

Now substitute \( x = y - 7 \) into Equation 1:
\[
2(y - 7) + 3y = 11
\]
\[
2y - 14 + 3y = 11
\]
\[
5y = 25
\]
\[
y = 5
\]

Substitute \( y = 5 \) into Equation 3:
\[
x = 5 - 7 = -2
\]

Thus, for part (c), the solution is:
\[
x = -2, \quad y = 5
\]

---

### Summary of Solutions:
- **Part a**: \( x = 6, y = 8 \)
- **Part b**: \( y \) is undetermined.
- **Part c**: \( x = -2, y = 5 \)

Would you like more detailed explanations or have any questions?

Here are 5 related questions to further practice:
1. How would you solve a system of linear equations using matrix inversion?
2. Can you express matrix addition geometrically or graphically?
3. What is the determinant of a matrix, and how does it relate to the solutions of linear systems?
4. How do you determine if a system of equations has one solution, no solution, or infinite solutions?
5. What is the method of Gaussian elimination, and how does it help solve matrix equations?

**Tip:** When solving systems of equations, always look for symmetries or patterns that can simplify calculations before diving into complex algebraic manipulations.

Tentukan nilai x dan y pada setiap persamaan matriks berikut.

Learn how to solve matrix equations and find the values of x and y. This problem involves matrix addition and solving systems of linear equations. Suitable for high school students in Grades 10-12.

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