which value, when placed in the box, would result in a system of equations with infinitely many solutions?

$y = -2x + 4$

$6x + 3y = \square$

-12
-4
4
12

Question

which value, when placed in the box, would result in a system of equations with infinitely many solutions?

$y = -2x + 4$

$6x + 3y = \square$

-12
-4
4
12

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 Equations", "Systems of Equations" ], "new_concepts": [], "current_concepts": [ "Systems of Linear Equations", "Systems of Equations", "Infinitely Many Solutions" ] } ## Rewrite the first equation in standard form $$ \begin{aligned} y &= -2x + 4 \ 2x + y &= 4 \end{aligned} $$ ## Compare with the second equation $$ \begin{aligned} 6x + 3y &= \square \ 3(2x + y) &= \square \end{aligned} $$ ## Solve for the missing value $$ \begin{aligned} \square &= 3(4) \ \square &= 12 \end{aligned} $$

-12

-4

4

12

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

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QUESTION IMAGE

Question

Explanation:

Rewrite the first equation in standard form

Compare with the second equation

Solve for the missing value

Answer: