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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Linear Equations in Two Variables", "Evaluating Algebraic Expressions" ], "new_concepts": [ "Systems of Linear Equations", "Verifying Solutions to Systems" ], "current_concepts": [ "Linear Equations in Two Variables", "Evaluating Algebraic Expressions", "Systems of Linear Equations", "Verifying Solutions to Systems" ] } ## Identify the system and point We are given the following system of linear equations: $$ \begin{cases} 3x - 3y = -3 \ -3x + 3y = 3 \end{cases} $$ We need to determine if the point $(2, 3)$ lies on both lines by substituting $x = 2$ and $y = 3$. ## Substitute into the first equation Using the *Evaluating Algebraic Expressions* and *Linear Equations in Two Variables* knowledge points $$ \begin{aligned} 3x - 3y &= -3 \ 3(2) - 3(3) &= 6 - 9 \ &= -3 \end{aligned} $$ Since $-3 = -3$, the point $(2, 3)$ satisfies the first equation. ## Substitute into the second equation Using the *Evaluating Algebraic Expressions* and *Linear Equations in Two Variables* knowledge points $$ \begin{aligned} -3x + 3y &= 3 \ -3(2) + 3(3) &= -6 + 9 \ &= 3 \end{aligned} $$ Since $3 = 3$, the point $(2, 3)$ satisfies the second equation. ## Determine the final outcome Since the ordered pair $(2, 3)$ satisfies both equations, it lies on both lines in the system.

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

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Explanation:

Identify the system and point

Substitute into the first equation

Substitute into the second equation

Determine the final outcome

Answer: