which solution is valid within the context of the situation?

(19,6)
(17.5,5)
(30,-10)
(10,15)

Question

which solution is valid within the context of the situation?

(19,6)
(17.5,5)
(30,-10)
(10,15)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Systems of Linear Inequalities", "Graphical Solutions", "Real-world Constraints" ], "new_concepts": [], "current_concepts": [ "Systems of Linear Inequalities", "Graphical Solutions", "Real-world Constraints" ] } ## Identify the constraints from the graph $$ \begin{aligned} &\text{Feasible region is shaded in the first quadrant (dark grey region).}\ &x \ge 0, \quad y \ge 0 \quad (\text{Real-world context requires non-negative values}) \end{aligned} $$ ## Evaluate the given options against constraints $$ \begin{aligned} &(30, -10): \quad y = -10 < 0 \quad (\text{Invalid})\ &(10, 15): \quad \text{Located well above the shaded region boundary}\ &(17.5, 5): \quad \text{Non-integer values; real-world context typically requires integers}\ &(19, 6): \quad \text{Lies within the shaded region; consists of valid whole numbers} \end{aligned} $$ ## Confirm the valid solution $$ (x, y) = (19, 6) $$

(A) (19,6)

(B) (17.5,5)

(C) (30,-10)

(D) (10,15)

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

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QUESTION IMAGE

Question

Explanation:

Identify the constraints from the graph

Evaluate the given options against constraints

Confirm the valid solution

Answer: