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The problem provided involves a system of linear equations. Here's the system:

\[
2x + 3y = 8
\]
\[
3x + 5y = 14
\]

You are asked to find \( 4a - 3b \), where \( x = a \) and \( y = b \) are solutions to the system.

### Step 1: Solve the system of equations
We will solve the system using the substitution or elimination method. Let’s use the elimination method.

1. First, multiply the first equation by 3 and the second equation by 2 to align the coefficients of \( x \):

\[
(2x + 3y = 8) \times 3 \Rightarrow 6x + 9y = 24
\]
\[
(3x + 5y = 14) \times 2 \Rightarrow 6x + 10y = 28
\]

### Step 2: Subtract the equations
Now, subtract the first modified equation from the second:

\[
(6x + 10y) - (6x + 9y) = 28 - 24
\]
\[
6x + 10y - 6x - 9y = 4
\]
\[
y = 4
\]

### Step 3: Substitute \( y = 4 \) back into one of the original equations
Substitute \( y = 4 \) into the first equation \( 2x + 3y = 8 \):

\[
2x + 3(4) = 8
\]
\[
2x + 12 = 8
\]
\[
2x = 8 - 12
\]
\[
2x = -4
\]
\[
x = -2
\]

Thus, \( x = -2 \) and \( y = 4 \).

### Step 4: Calculate \( 4a - 3b \)
Given \( x = a = -2 \) and \( y = b = 4 \), we need to find \( 4a - 3b \):

\[
4a - 3b = 4(-2) - 3(4)
\]
\[
= -8 - 12
\]
\[
= -20
\]

### Final Answer:
The value of \( 4a - 3b \) is \( -20 \).

Would you like more details or have any questions?

---

Here are 5 related questions to expand on this concept:

1. How can you solve this system of equations using the substitution method?
2. What happens if you add the two equations instead of subtracting them?
3. Can you generalize this method for any system of two linear equations?
4. How would you interpret the solution geometrically?
5. What if one of the equations was non-linear? How would you approach it?

**Tip:** When solving systems of equations, always check your solution by substituting the values back into the original equations to ensure correctness.

Diketahui system persamaan linier dua variable berikut:
2x + 3y = 8
3x + 5y = 14, jika adalah penyelesaian dari system tersebut x = a, y = b, maka tentukan 4a - 3b!

Learn how to solve the system of linear equations 2x + 3y = 8 and 3x + 5y = 14, and find the value of 4a - 3b where x = a and y = b. This problem involves key algebraic concepts and methods like elimination and substitution. Suitable for Grades 9-11.

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