systems of inequalities: practice which system of inequalities has the following graph as its solution? $\circ \begin{cases} x 3 \\ y \ge 2x - 5 \end{cases}$ $\circ \begin{cases} x 3 \\ y \le 2x - 5 \end{cases}$ $\circ \begin{cases} x

Question

systems of inequalities: practice

which system of inequalities has the following graph as its solution?

\\(\circ \

\begin{cases} x > 3 \\\\ y \\ge 2x - 5 \\end{cases}

\\)

\\(\circ \

\begin{cases} x > 3 \\\\ y \\le 2x - 5 \\end{cases}

\\)

\\(\circ \

\begin{cases} x < 3 \\\\ y \\ge 2x - 5 \\end{cases}

\\)

\\(\circ \

\begin{cases} x < 3 \\\\ y \\le 2x - 5 \\end{cases}

\\)

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" ], "new_concepts": [], "current_concepts": [ "Systems of Linear Inequalities", "Graphical Solutions", "Linear Functions" ] } ## Identify the vertical boundary line $$ \begin{aligned} &\text{Boundary line: } x = 3 \quad (\text{dashed line})\ &\text{Shaded region is to the left of } x = 3\ &\text{Inequality: } x < 3 \end{aligned} $$ ## Identify the slanted boundary line $$ \begin{aligned} &\text{Boundary line: } y = 2x - 5 \quad (\text{solid line})\ &\text{Shaded region is above/left of the line}\ &\text{Test point } (3, 3) \text{ in shaded region: } 3 \ge 2(3) - 5 \implies 3 \ge 1 \quad (\text{True})\ &\text{Inequality: } y \ge 2x - 5 \end{aligned} $$ ## Combine the inequalities $$ \begin{cases} x < 3 \ y \ge 2x - 5 \end{cases} $$

(A) $\begin{cases} x > 3 \ y \ge 2x - 5 \end{cases}$

(B) $\begin{cases} x > 3 \ y \le 2x - 5 \end{cases}$

(C) $\begin{cases} x < 3 \ y \ge 2x - 5 \end{cases}$

(D) $\begin{cases} x < 3 \ y \le 2x - 5 \end{cases}$

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

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QUESTION IMAGE

Question

Explanation:

Identify the vertical boundary line

Identify the slanted boundary line

Combine the inequalities

Answer: