the system of equations graphed below can be classified as

consistent, independent
consistent, dependent
inconsistent

Question

the system of equations graphed below can be classified as

consistent, independent
consistent, dependent
inconsistent

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Linear Equations", "Linear Graphs" ], "new_concepts": [ "Systems of Equations Classification", "Consistent and Independent Systems" ], "current_concepts": [ "Linear Equations", "Linear Graphs", "Systems of Equations Classification", "Consistent and Independent Systems" ] } ## Analyze the graphed system Using the *Linear Graphs* and *Linear Equations* knowledge points $$ \begin{aligned} &\text{Line 1 passes through: } (0, 3) \text{ and } (2, 2)\ &\text{Line 2 passes through: } (0, -4) \text{ and } (2, 2)\ &\text{Intersection point: } (2, 2) \end{aligned} $$ ## Classify the system of equations A system of linear equations is classified based on the number of solutions it has: - **Consistent**: The system has at least one solution (the lines intersect). - **Inconsistent**: The system has no solutions (the lines are parallel and distinct). - **Independent**: The system has exactly one unique solution (the lines intersect at a single point). - **Dependent**: The system has infinitely many solutions (the lines are identical). Since the graphed lines intersect at exactly one unique point $(2, 2)$, the system is consistent and independent.

Consistent, Independent

Consistent, Dependent

Inconsistent

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Systems of Equations Classification" ] }

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Explanation:

Analyze the graphed system

Classify the system of equations

Answer: