Math Problem Statement

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

Solution

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

2a - 8b = 12 \\ 3a - 6b = 9 \\ -a + 2b = -4 \end{cases}$$ Let's solve this system step by step. ### Step 1: Simplify the Equations Observe if there are any simplifications: 1. The first equation is $$2a - 8b = 12$$. 2. The second equation is $$3a - 6b = 9$$, which can be simplified by dividing all terms by 3: $$a - 2b = 3$$ 3. The third equation is already $$-a + 2b = -4$$. Now, we have the following simplified system: $$\begin{cases} 2a - 8b = 12 \\ a - 2b = 3 \\ -a + 2b = -4 \end{cases}$$ ### Step 2: Substitute or Eliminate Variables Let's add the second and third equations together to see if we can eliminate $$a$$: $$(a - 2b) + (-a + 2b) = 3 + (-4)$$ This results in: $$0 = -1$$ This contradiction ($$0 = -1$$) indicates that the system of equations is **inconsistent**, meaning there is no solution that satisfies all three equations simultaneously. ### Conclusion This system has no solution due to inconsistency among the equations. Would you like further details on any part of the solution? --- Here are some related questions for deeper understanding: 1. What does it mean for a system of equations to be inconsistent? 2. How can we determine if a system of equations has a unique solution, no solution, or infinitely many solutions? 3. What methods can be used to solve a system of linear equations, and when are each most appropriate? 4. How can we identify dependent or independent equations in a system? 5. What is the significance of finding a contradiction in a system of equations? **Tip:** Always check for simplifications in each equation of a system. This can help identify inconsistencies or dependencies early in the process.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations
Inconsistency in Equations

Formulas

Substitution or elimination methods for solving linear equations

Theorems

No-solution theorem for inconsistent systems

Suitable Grade Level

Grade 10-12

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