verify whether the given point is a solution for the system of linear equations.
a. $y = 4x + 9$ and $y = -3x - 5$; $(-2, 1)$

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "System of Equations" ], "new_concepts": [], "current_concepts": [ "System of Equations", "Linear Equation Solving" ] } ## Substitute the point into the first equation $$ \begin{aligned} &\text{Point: } (-2, 1) \implies x = -2, \quad y = 1\ &\text{Equation 1: } y = 4x + 9\ &1 = 4(-2) + 9\ &1 = -8 + 9\ &1 = 1 \quad (\text{True}) \end{aligned} $$ ## Substitute the point into the second equation $$ \begin{aligned} &\text{Equation 2: } y = -3x - 5\ &1 = -3(-2) - 5\ &1 = 6 - 5\ &1 = 1 \quad (\text{True}) \end{aligned} $$ ## Determine the final verification result $$ \text{Since } (-2, 1) \text{ satisfies both equations, it is a solution.} $$ Yes, the point $(-2, 1)$ is a solution for the given system of linear equations. { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "System of Equations" ] }

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Explanation:

Substitute the point into the first equation

Substitute the point into the second equation

Determine the final verification result

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