https://file.aiquickdraw.com/mathbot/file/1726118257050x3rnt6l9.jpg

The system of linear equations (SPL) provided in the image is:

\[
\begin{aligned}
1) \ 2a - 8b &= 12 \\
2) \ 3a - 6b &= 9 \\
3) \ -a + 2b &= -4
\end{aligned}
\]

To solve this system, I'll use either substitution, elimination, or matrix methods. Let's proceed step by step using the elimination method.

### Step 1: Simplify the equations (if necessary)
All equations are already in simplified form.

### Step 2: Use elimination or substitution
From equation (3):
\[
-a + 2b = -4 \quad \Rightarrow \quad a = 2b + 4
\]
Now, substitute \(a = 2b + 4\) into equations (1) and (2).

#### Substituting into equation (1):
\[
2(2b + 4) - 8b = 12
\]
Simplify:
\[
4b + 8 - 8b = 12
\]
\[
-4b + 8 = 12
\]
\[
-4b = 12 - 8
\]
\[
-4b = 4 \quad \Rightarrow \quad b = -1
\]

### Step 3: Find \(a\)
Now that we know \(b = -1\), substitute \(b = -1\) into \(a = 2b + 4\):
\[
a = 2(-1) + 4 = -2 + 4 = 2
\]

### Step 4: Verify the solution
Substitute \(a = 2\) and \(b = -1\) into equation (2) to verify:
\[
3a - 6b = 9
\]
\[
3(2) - 6(-1) = 6 + 6 = 12 \quad \text{(which is incorrect, meaning a contradiction or a mistake exists)}
\]

Let me recheck and resolve the system properly.It appears that there is no solution to the system of equations. This indicates that the system is inconsistent, meaning the three equations do not have a common solution for \(a\) and \(b\). In such cases, the system could represent parallel lines or equations that contradict each other, leading to no intersection or solution.

Let me know if you'd like more details on why this might happen or if you'd like further assistance.

Here are 5 follow-up questions to expand on this:
1. What does it mean when a system of equations has no solution?
2. How can you tell if a system of equations is inconsistent?
3. What methods are used to solve systems of linear equations?
4. Can a system of three equations in two variables have exactly one solution?
5. What are dependent and independent systems of linear equations?

**Tip**: Always double-check your work by substituting your solutions back into the original equations

Tentukan solusi SPL berikut: 2a - 8b = 12, 3a - 6b = 9, -a + 2b = -4

This tutorial explains how to solve the system of linear equations: 2a - 8b = 12, 3a - 6b = 9, and -a + 2b = -4 using algebraic methods. Key concepts covered include the substitution and elimination methods. Suitable for students in Grades 9-12.

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