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{ "quality": "blurry", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Linear Systems", "Number of Solutions", "Slope-Intercept Form" ], "current_concepts": [ "Linear Systems", "Number of Solutions", "Slope-Intercept Form" ] } ## Analyze the first system of equations $$ \begin{aligned} &L_1: x - 2y = 6 \implies y = \frac{1}{2}x - 3 \ &L_2: x + y = -2 \implies y = -x - 2 \ &m_1 = \frac{1}{2},\quad m_2 = -1 \implies m_1 e m_2 \end{aligned} $$ ## Analyze the second system of equations $$ \begin{aligned} &L_1: 3x + 5y = 9 \implies y = -\frac{3}{5}x + \frac{9}{5} \ &L_2: 6x + 10y = 18 \implies y = -\frac{6}{10}x + \frac{18}{10} = -\frac{3}{5}x + \frac{9}{5} \ &m_1 = m_2 = -\frac{3}{5},\quad b_1 = b_2 = \frac{9}{5} \end{aligned} $$ ## Analyze the third system of equations $$ \begin{aligned} &L_1: 2x - 5y = 30 \implies y = \frac{2}{5}x - 6 \ &L_2: 4x - 10y = 15 \implies y = \frac{4}{10}x - \frac{15}{10} = \frac{2}{5}x - \frac{3}{2} \ &m_1 = m_2 = \frac{2}{5},\quad b_1 = -6 e b_2 = -\frac{3}{2} \end{aligned} $$ ## Question 1 One solution ## Question 2 Infinite solutions ## Question 3 No solution { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Linear Systems" ] }

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Analyze the first system of equations

Analyze the second system of equations

Analyze the third system of equations

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Question 1

Question 2

Question 3