https://file.aiquickdraw.com/mathbot/file/1726719069988jwrfoalf.jpg

The given problem involves a matrix equation:

\[
\begin{pmatrix}
\frac{4}{3} \\
x
\end{pmatrix}
+
\begin{pmatrix}
x \\
y
\end{pmatrix}
=
\begin{pmatrix}
6 \\
7
\end{pmatrix}
\]

We are asked to find the value of \( 2x + y \).

### Step 1: Solve for \( x \) and \( y \)

From the matrix addition, we can equate the corresponding components:

1. First equation (top row):
   \[
   \frac{4}{3} + x = 6
   \]
   Solving for \( x \):
   \[
   x = 6 - \frac{4}{3} = \frac{18}{3} - \frac{4}{3} = \frac{14}{3}
   \]

2. Second equation (bottom row):
   \[
   x + y = 7
   \]
   Substituting \( x = \frac{14}{3} \):
   \[
   \frac{14}{3} + y = 7
   \]
   Solving for \( y \):
   \[
   y = 7 - \frac{14}{3} = \frac{21}{3} - \frac{14}{3} = \frac{7}{3}
   \]

### Step 2: Calculate \( 2x + y \)

Now, we calculate \( 2x + y \):
\[
2x + y = 2 \times \frac{14}{3} + \frac{7}{3} = \frac{28}{3} + \frac{7}{3} = \frac{35}{3}
\]
\[
2x + y = \frac{35}{3} \approx 11.67
\]

Since the closest integer to \( 11.67 \) is 12, the answer is:

\[
\boxed{B} \, 12
\]

Would you like more details, or do you have any questions?

Here are five related questions:
1. How do you solve matrix addition problems in general?
2. Can you explain the properties of matrix addition and scalar multiplication?
3. What are other common types of matrix equations?
4. How do you handle equations involving fractions more efficiently?
5. How can you verify solutions to matrix equations?

**Tip:** Always double-check the addition and subtraction of fractions to avoid errors in algebraic manipulation.

Jika [4/3] + [x/y] = [6/7], nilai (2x + y) adalah ...

Learn how to solve a matrix equation with fractions, [4/3] + [x/y] = [6/7], and find the value of (2x + y). This problem covers algebraic matrix addition, solving linear equations, and fraction manipulation. Suitable for high school students in Grades 9-12.

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