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

1. $2a - 8b = 12$
2. $3a - 6b = 9$
3. $-a + 2b = -4$

Let me solve this system of equations step by step:

Step 1: Simplify the equations if needed

Equation (1): $2a - 8b = 12$
Equation (2): $3a - 6b = 9$
Equation (3): $-a + 2b = -4$

We will start by eliminating one variable, such as $a$.

Step 2: Eliminate $a$

From Equation (3):
$-a + 2b = -4 \implies a = 2b + 4$

Substitute $a = 2b + 4$ into Equations (1) and (2):

1. Substituting into Equation (1):
   $2(2b + 4) - 8b = 12$
   $4b + 8 - 8b = 12$
   $-4b + 8 = 12$
   $-4b = 4$
   $b = -1$

2. Substituting $b = -1$ into Equation (3) for $a$:
   $a = 2(-1) + 4$
   $a = 2$

Step 3: Verify the solution

Substitute $a = 2$ and $b = -1$ into all three equations:

1. Equation (1):
   $2(2) - 8(-1) = 12$
   $4 + 8 = 12$ ✅

2. Equation (2):
   $3(2) - 6(-1) = 9$
   $6 + 6 = 9$ ✅

3. Equation (3):
   $-2 + 2(-1) = -4$
   $-2 - 2 = -4$ ✅

Solution

The solution is:
$a = 2, \, b = -1$

Would you like further details or explanations? Here are related questions to expand on this topic:

1. How can this solution be verified graphically?
2. What methods can be used to solve systems of equations other than substitution?
3. Can the determinant method (Cramer's rule) be applied to this problem?
4. How do dependent and independent systems of equations differ?
5. How can systems with no solutions or infinitely many solutions be identified?

Tip: Always substitute back your solution into the original equations to ensure its validity!