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The image contains a system of linear equations involving three variables, \(x\), \(y\), and \(z\). The problem asks to determine the values of \(x\), \(y\), and \(z\) that satisfy the following matrix equation:

\[
\begin{pmatrix} 3 & 3x \\ 4 & y \end{pmatrix} - \begin{pmatrix} 2 & y + x \\ y + 2 & z \end{pmatrix} = \begin{pmatrix} 1 & 7 \\ 3 & -4 \end{pmatrix}
\]

We can solve this by expanding both sides and setting up equations from the components.

### Step-by-step process:

#### 1. Matrix on the left-hand side:
\[
\begin{pmatrix} 3 & 3x \\ 4 & y \end{pmatrix}
\]

#### 2. Matrix subtracted from it:
\[
\begin{pmatrix} 2 & y + x \\ y + 2 & z \end{pmatrix}
\]

#### 3. Perform matrix subtraction:
\[
\begin{pmatrix} 3 & 3x \\ 4 & y \end{pmatrix} - \begin{pmatrix} 2 & y + x \\ y + 2 & z \end{pmatrix} = \begin{pmatrix} 3-2 & 3x-(y+x) \\ 4-(y+2) & y - z \end{pmatrix}
\]
This simplifies to:
\[
\begin{pmatrix} 1 & 3x - y - x \\ 4 - y - 2 & y - z \end{pmatrix}
\]
Which gives:
\[
\begin{pmatrix} 1 & 2x - y \\ 2 - y & y - z \end{pmatrix}
\]

#### 4. Equate to the matrix on the right-hand side:
\[
\begin{pmatrix} 1 & 7 \\ 3 & -4 \end{pmatrix}
\]

Now, we have the following system of equations:
- \( 1 = 1 \) (which is trivially true)
- \( 2x - y = 7 \)
- \( 2 - y = 3 \)
- \( y - z = -4 \)

#### 5. Solve the system of equations:
From \(2 - y = 3\):
\[
y = -1
\]

Substitute \(y = -1\) into the second equation \(2x - y = 7\):
\[
2x - (-1) = 7 \quad \Rightarrow \quad 2x + 1 = 7 \quad \Rightarrow \quad 2x = 6 \quad \Rightarrow \quad x = 3
\]

Substitute \(y = -1\) into the third equation \(y - z = -4\):
\[
-1 - z = -4 \quad \Rightarrow \quad -z = -3 \quad \Rightarrow \quad z = 3
\]

Thus, the solution is:
\[
x = 3, \quad y = -1, \quad z = 3
\]

#### 6. Check the options:
The correct answer is option **C**: \( (3, -1, 3) \).

---

Would you like more details on this solution or have any further questions?

### Related Questions:
1. What is the general method for solving systems of linear equations involving matrices?
2. How do you verify matrix operations such as addition and subtraction?
3. Can matrix equations like these be solved using determinants or inverses?
4. How do you represent a system of linear equations in matrix form?
5. What are some real-world applications of solving systems of equations using matrices?

### Tip:
When solving matrix equations, always ensure that the operations (addition, subtraction) are performed element-wise and that matrices are of the same dimensions to be compatible for such operations.

Tentukan nilai x, y dan z yang memenuhi persamaan 

[3, 3x; 4, y] - [2, y+x; y+2, z] = [1, 7; 3, -4]

Discover how to solve a complex system of linear equations using matrix operations. This example includes detailed step-by-step explanations of matrix subtraction and solving for variables x, y, and z.

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