Math Problem Statement
The system 4 6 8 2 3 8 x y x y is a/an _____________ system.
Solution
The given system of equations is:
2x - 3y &= 8 \\ 4x + 6y &= -8 \end{aligned}$$ This is a **dependent system** of linear equations because both equations represent the same line. To see this, you can multiply the first equation by 2, and you'll get the second equation: $$\begin{aligned} 2(2x - 3y) &= 2(8) \\ 4x - 6y &= 16 \end{aligned}$$ But the second equation is $$4x + 6y = -8$$, so these two equations represent parallel lines that never intersect, meaning that the system is inconsistent, and they are contradictory, implying **no solution**. Thus, the system is **inconsistent**. Would you like more details or further clarification? Here are 5 related questions you might explore: 1. How do you classify systems of equations as dependent, independent, or inconsistent? 2. What is the graphical interpretation of an inconsistent system? 3. What is the difference between dependent and inconsistent systems? 4. How do you solve a system of equations by substitution? 5. What are the methods to determine if a system is consistent or inconsistent? **Tip:** When solving a system of linear equations, try to simplify or multiply the equations to check if one is a multiple of the other—this often reveals the nature of the system.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Equations
System of Equations
Consistency and Dependency
Formulas
General form of a linear equation: ax + by = c
Theorems
Classification of systems of equations: Dependent, Independent, and Inconsistent
Suitable Grade Level
Grades 9-12
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