for which system of inequalities is $(3,-7)$ a solution?

$\begin{cases} x + y

Question

for which system of inequalities is $(3,-7)$ a solution?

$\begin{cases} x + y < -4 \\ 3x + 2y < -5 \end{cases}$

$\begin{cases} x + y \le -4 \\ 3x + 2y < -5 \end{cases}$

$\begin{cases} x + y < -4 \\ 3x + 2y \le -5 \end{cases}$

$\begin{cases} x + y \le -4 \\ 3x + 2y \le -5 \end{cases}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Inequalities" ], "new_concepts": [], "current_concepts": [ "Linear Inequalities", "Systems of Linear Inequalities" ] } ## Evaluate the first inequality expression $$ \begin{aligned} &\text{Substitute } (x, y) = (3, -7) \text{ into } x + y:\ &3 + (-7) = -4 \end{aligned} $$ ## Evaluate the second inequality expression $$ \begin{aligned} &\text{Substitute } (x, y) = (3, -7) \text{ into } 3x + 2y:\ &3(3) + 2(-7) = 9 - 14 = -5 \end{aligned} $$ ## Determine the correct system of inequalities $$ \begin{aligned} &\text{Since } x + y = -4 \text{ and } 3x + 2y = -5:\ &-4 \le -4 \quad (\text{True})\ &-5 \le -5 \quad (\text{True})\ &\text{Therefore, the system must use } \le \text{ for both inequalities:} \ &\begin{cases} x + y \le -4 \ 3x + 2y \le -5 \end{cases} \end{aligned} $$

(A) $\begin{cases} x + y < -4 \ 3x + 2y < -5 \end{cases}$

(B) $\begin{cases} x + y \le -4 \ 3x + 2y < -5 \end{cases}$

(C) $\begin{cases} x + y < -4 \ 3x + 2y \le -5 \end{cases}$

(D) $\begin{cases} x + y \le -4 \ 3x + 2y \le -5 \end{cases}$

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

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QUESTION IMAGE

Question

Explanation:

Evaluate the first inequality expression

Evaluate the second inequality expression

Determine the correct system of inequalities

Answer: