system c

line 1: $y = \frac{3}{2}x + 1$

line 2: $y = \frac{3}{2}x + 3$

this system of equations is:
- inconsistent
- consistent dependent
- consistent independent

this means the system has:
- a unique solution
solution: ( , )
- infinitely many solutions
- no solution

Question

system c

line 1: $y = \frac{3}{2}x + 1$

line 2: $y = \frac{3}{2}x + 3$

this system of equations is:
- inconsistent
- consistent dependent
- consistent independent

this means the system has:
- a unique solution
  solution: ( , )
- infinitely many solutions
- no solution

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Systems of Linear Equations", "Inconsistent Systems" ], "new_concepts": [], "current_concepts": [ "Systems of Linear Equations", "Inconsistent Systems" ] } ## Compare slopes and y-intercepts $$ \begin{aligned} &m_1 = \frac{3}{2},\quad b_1 = 1\ &m_2 = \frac{3}{2},\quad b_2 = 3\ &m_1 = m_2 \quad \text{and} \quad b_1 eq b_2 \end{aligned} $$ ## Determine system classification and solutions $$ \begin{aligned} &\text{Since the lines are parallel and distinct:}\ &\text{System classification} = \text{inconsistent}\ &\text{Number of solutions} = \text{no solution} \end{aligned} $$ ## Question 1 inconsistent

consistent dependent

consistent independent ## Question 2 a unique solution

infinitely many solutions

no solution

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

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QUESTION IMAGE

Question

Explanation:

Compare slopes and y-intercepts

Determine system classification and solutions

Answer:

Question 1

Question 2