1. 7x+3y=21
   x+3y=33 
ket: x+y = 2, selesaikan dengan pldv matriks

To solve the system of equations using the method of matrices (PLDV), we can express the equations in matrix form:

1. The original equations are:
   \[
   7x + 3y = 21 \quad (1)
   \]
   \[
   x + 3y = 33 \quad (2)
   \]

2. Rewrite in matrix form \(AX = B\):
   \[
   \begin{bmatrix}
   7 & 3 \\
   1 & 3
   \end{bmatrix}
   \begin{bmatrix}
   x \\
   y
   \end{bmatrix}
   =
   \begin{bmatrix}
   21 \\
   33
   \end{bmatrix}
   \]

3. Let \(A = \begin{bmatrix} 7 & 3 \\ 1 & 3 \end{bmatrix}\), \(X = \begin{bmatrix} x \\ y \end{bmatrix}\), and \(B = \begin{bmatrix} 21 \\ 33 \end{bmatrix}\).

4. Calculate the inverse of matrix \(A\):
   - The determinant of \(A\) is:
     \[
     \text{det}(A) = 7 \cdot 3 - 3 \cdot 1 = 21 - 3 = 18
     \]

   - The inverse \(A^{-1}\) is given by:
     \[
     A^{-1} = \frac{1}{\text{det}(A)} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix} = \frac{1}{18} \begin{bmatrix} 3 & -3 \\ -1 & 7 \end{bmatrix}
     \]

5. Now, multiply \(A^{-1}\) with \(B\):
   \[
   X = A^{-1}B = \frac{1}{18} \begin{bmatrix} 3 & -3 \\ -1 & 7 \end{bmatrix} \begin{bmatrix} 21 \\ 33 \end{bmatrix}
   \]

6. Calculating \(X\):
   \[
   \begin{bmatrix} 3 \cdot 21 - 3 \cdot 33 \\ -1 \cdot 21 + 7 \cdot 33 \end{bmatrix} = \begin{bmatrix} 63 - 99 \\ -21 + 231 \end{bmatrix} = \begin{bmatrix} -36 \\ 210 \end{bmatrix}
   \]

   Now divide by 18:
   \[
   X = \begin{bmatrix} -2 \\ 11.67 \end{bmatrix}
   \]

7. Therefore, the solution is:
   \[
   x = -2, \quad y \approx 11.67
   \]

If you need further details or have any questions about the process, let me know!

### Related Questions:
1. What would the solution be if the second equation were changed?
2. How can you verify the solution graphically?
3. What happens if the determinant of matrix \(A\) is zero?
4. Can you explain how to find the inverse of a matrix in general?
5. How can you apply this method to a system of three equations?

### Tip:
Always check the solution by substituting back into the original equations to ensure accuracy.

1. 7x+3y=21; x+3y=33; ket: x+y = 2, selesaikan dengan pldv matriks

Explore the step-by-step solution for the system of equations 7x + 3y = 21 and x + 3y = 33 using matrix inversion. This detailed guide covers key concepts in linear algebra, including how to calculate the determinant and the inverse of a matrix. Ideal for students in Grades 10-12.

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