7) \-4x + y = 6\
\-5x - y = 21\

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Substitution Method", "Systems of Equations" ], "new_concepts": [ "Elimination Method" ], "current_concepts": [ "Systems of Equations", "Substitution Method", "Elimination Method" ] } ## Write the system of equations $$ \begin{aligned} -4x + y &= 6 \quad \text{(Equation 1)} \ -5x - y &= 21 \quad \text{(Equation 2)} \end{aligned} $$ ## Add the equations to eliminate y $$ \begin{aligned} (-4x + y) + (-5x - y) &= 6 + 21 \ -9x &= 27 \ x &= -3 \end{aligned} $$ ## Substitute x to solve for y $$ \begin{aligned} -4(-3) + y &= 6 \ 12 + y &= 6 \ y &= -6 \end{aligned} $$ $(-3, -6)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Systems of Equations" ] }

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Explanation:

Write the system of equations

Add the equations to eliminate y

Substitute x to solve for y

Answer: