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The problem provided is in Indonesian, and it can be translated as:

"A line with the equation \( ax + by = 8 \) passes through the points \( (3, -2) \) and \( (2, 4) \). The values of \( a \) and \( b \), respectively, are . . ."

### Steps to solve:

We are given the general form of the line equation \( ax + by = 8 \) and two points: \( (3, -2) \) and \( (2, 4) \). We need to find the values of \( a \) and \( b \).

1. **Substitute the points into the equation**:

   - For the point \( (3, -2) \):
   \[
   a(3) + b(-2) = 8 \implies 3a - 2b = 8 \tag{1}
   \]
   
   - For the point \( (2, 4) \):
   \[
   a(2) + b(4) = 8 \implies 2a + 4b = 8 \tag{2}
   \]

2. **Solve the system of equations**:

   From equation (1):
   \[
   3a - 2b = 8
   \]

   From equation (2):
   \[
   2a + 4b = 8
   \]
   
   Now, we can solve these two simultaneous equations to find \( a \) and \( b \).

- Multiply equation (2) by 2 to match the coefficient of \( a \) with that in equation (1):
  \[
  4a + 8b = 16 \tag{3}
  \]

- Subtract equation (1) from equation (3):
  \[
  (4a + 8b) - (3a - 2b) = 16 - 8
  \]
  Simplifying:
  \[
  a + 10b = 8 \tag{4}
  \]

3. **Solve for \( a \) and \( b \)**:

Now, from equation (4):
   - Rearrange: \( a = 8 - 10b \)
   - Substitute this into equation (2):
     \[
     2(8 - 10b) + 4b = 8
     \]
     Simplifying:
     \[
     16 - 20b + 4b = 8 \implies -16b = -8 \implies b = \frac{1}{2}
     \]

   - Substitute \( b = \frac{1}{2} \) into \( a = 8 - 10b \):
     \[
     a = 8 - 10\left(\frac{1}{2}\right) = 8 - 5 = 3
     \]

### Final Answer:
The values of \( a \) and \( b \) are \( 3 \) and \( \frac{1}{2} \), respectively.

Would you like more details on the solution process or have any other questions?

Here are 5 related questions to consider:
1. How do you solve a system of linear equations using substitution?
2. Can you find the equation of the line in slope-intercept form from the two points given?
3. How does the standard form of a line equation relate to its slope and intercept?
4. How can you verify that the points \( (3, -2) \) and \( (2, 4) \) satisfy the final equation \( 3x + \frac{1}{2}y = 8 \)?
5. What are other methods to solve systems of equations, such as elimination?

**Tip**: Always double-check by substituting the values back into the original equations to confirm the solution is correct.

Garis dengan persamaan ax + by = 8 melalui titik (3, -2) dan (2, 4). Nilai a dan b berturut-turut adalah . . .

Find the values of a and b in the equation ax + by = 8, passing through points (3, -2) and (2, 4). This problem demonstrates how to solve simultaneous linear equations using substitution or elimination methods.

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