6) $y = 5x - 7$
$-3x - 2y = -12$

Question

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": [], "current_concepts": [ "Substitution Method", "Systems of Equations" ] } ## Set up the system of equations $$ \begin{cases} y = 5x - 7 & \text{(Equation 1)} \ -3x - 2y = -12 & \text{(Equation 2)} \end{cases} $$ ## Substitute Equation 1 into Equation 2 $$ \begin{aligned} -3x - 2(5x - 7) &= -12 \ -3x - 10x + 14 &= -12 \ -13x + 14 &= -12 \ -13x &= -26 \ x &= 2 \end{aligned} $$ ## Solve for y using Equation 1 $$ \begin{aligned} y &= 5(2) - 7 \ y &= 10 - 7 \ y &= 3 \end{aligned} $$ $(2, 3)$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Systems of Equations" ] }

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Question

Explanation:

Set up the system of equations

Substitute Equation 1 into Equation 2

Solve for y using Equation 1

Answer: