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{ "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" ], "new_concepts": [ "Classification of Linear Systems" ], "current_concepts": [ "Systems of Linear Equations", "Classification of Linear Systems" ] } ## Formulate the system of equations for Question 5 $$ \begin{cases} x + y = 25 \ 20x + 40y = 900 \end{cases} $$ ## Solve the system for Question 5 $$ \begin{aligned} x &= 25 - y \ 20(25 - y) + 40y &= 900 \ 500 - 20y + 40y &= 900 \ 20y &= 400 \ y &= 20 \ x &= 5 \end{aligned} $$ ## Analyze the system for Question 6 $$ \begin{cases} 7y = 7x + 21 \implies y = x + 3 \ y = x + 3 \end{cases} $$ Both equations represent the same line, meaning there are infinitely many solutions. ## Question 5 8 self-propelled mowers and 17 riding mowers

5 self-propelled mowers and 20 riding mowers

18 self-propelled mowers and 7 riding mowers

12 self-propelled mowers and 13 riding mowers ## Question 6 Consistent and Dependent

Inconsistent

Consistent and Independent

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

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Explanation:

Formulate the system of equations for Question 5

Solve the system for Question 5

Analyze the system for Question 6

Answer:

Question 5

Question 6