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From the image you've uploaded, there are two separate matrix equations given. Let's solve each one step-by-step:

### Problem 6
Given matrices \(A\) and \(B\) as follows:
\[ A = \begin{bmatrix} 5 & 7 \\ 2 & 9 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} 5 & x \\ 2 & y \end{bmatrix} \]
It is stated that \(2A = B\).

To find this relation:
\[ 2A = 2 \begin{bmatrix} 5 & 7 \\ 2 & 9 \end{bmatrix} = \begin{bmatrix} 10 & 14 \\ 4 & 18 \end{bmatrix} \]
Comparing this with \(B\), we set:
\[ \begin{bmatrix} 10 & 14 \\ 4 & 18 \end{bmatrix} = \begin{bmatrix} 5 & x \\ 2 & y \end{bmatrix} \]
From here, we solve:
- For \(x\), \(14 = x\).
- For \(y\), \(18 = y\).

Additionally, calculate:
- \(2x + y\)
- \(2x + 4y\)

**Calculations:**
- \(2x + y = 2(14) + 18 = 28 + 18 = 46\)
- \(2x + 4y = 2(14) + 4(18) = 28 + 72 = 100\)

### Problem 7
Given matrices \(M\) and \(N\) as:
\[ M = \begin{bmatrix} q-4 & -8 & 2d-3 \\ b & 2c & -13 \end{bmatrix} \quad \text{and} \quad N = \begin{bmatrix} 3a & -8 & -11 \\ 2b-5 & 3c+8 & -13 \end{bmatrix} \]
It's given \(M = N\).

From this equality:
1. \(q-4 = 3a\)
2. \(2d-3 = -11\) implies \(2d = -8\) so \(d = -4\).
3. \(b = 2b - 5\) implies \(b = 5\).
4. \(2c = 3c + 8\) implies \(c = -8\).

Finally, find \(2a + 2b + 9c\):
- \(2a = \frac{2}{3}(q-4)\)
- \(2b = 2 \times 5 = 10\)
- \(9c = 9 \times (-8) = -72\)

**Calculation:**
- \(2a + 2b + 9c = \frac{2}{3}(q-4) + 10 - 72\)

Would you like further details or have any questions on these problems?

Here are some additional questions and a

6. Diketahui dua matriks A dan B sebagai berikut: A = [ [5, 7], [2, 9] ], B = [ [5, x], [2, y] ]. Jika 2A = B, tentukan: a) Nilai x dan y, b) Nilai 2x + y, c) Nilai 2x + 4y. 7. Diketahui matriks sebagai berikut: M = [ [q-4, -8, 2d-3], [b, 2c, -13] ], N = [ [3a, -8, 11], [2b-5, 3c+8, -13] ]. Jika M = N, tentukan: a) Nilai a, b, dan c, b) Nilai 2a + 3b + 9c.

Learn how to solve matrix equations involving matrices A, B, M, and N with given conditions like 2A = B and M = N. This problem focuses on matrix algebra, system of equations, and basic matrix operations. Suitable for students in Grades 10-12.

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