state the coordinates of a point in the solution set.

\y

Question

state the coordinates of a point in the solution set.

\y < -\frac{2}{3}x + 5\
\y \ge \frac{4}{3}x - 1\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Linear Inequalities", "System of Inequalities", "Graphical Solutions" ], "new_concepts": [], "current_concepts": [ "Linear Inequalities", "System of Inequalities", "Graphical Solutions" ] } ## Identify the system of inequalities $$ \begin{aligned} &y < -\frac{2}{3}x + 5 \ &y \ge \frac{4}{3}x - 1 \end{aligned} $$ ## Test a candidate coordinate point $$ \begin{aligned} &\text{Let } (x, y) = (0, 0): \ &0 < -\frac{2}{3}(0) + 5 \implies 0 < 5 \quad (\text{True}) \ &0 \ge \frac{4}{3}(0) - 1 \implies 0 \ge -1 \quad (\text{True}) \end{aligned} $$ ## Verify the selected point $$ (0, 0) \text{ satisfies both inequalities.} $$ State the coordinates of a point in the solution set. $(0, 0)$ { "elements": [ { "type": "inequality", "params": [{"js": "-2/3*x + 5", "latex": "y < -\frac{2}{3}x + 5"}, [1, 2]], "properties": { "inverse": false, "strict": true, "strokeColor": "#8C55F2", "fillColor": "rgba(140, 85, 242, 0.15)" } }, { "type": "inequality", "params": [{"js": "4/3*x - 1", "latex": "y \ge \frac{4}{3}x - 1"}, [-1, 2]], "properties": { "inverse": true, "strict": false, "strokeColor": "#5583F2", "fillColor": "rgba(85, 131, 242, 0.15)" } }, { "type": "point", "params": [[0, 0]], "properties": { "name": "(0,0)", "size": 4, "color": "#F2557F", "withLabel": true } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "System of Inequalities" ] }

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Question

Explanation:

Identify the system of inequalities

Test a candidate coordinate point

Verify the selected point

Answer: