determine how many solutions the system has. if it has one solution, state what the solution is.

\\begin{aligned}
2x - 3y &= -9 \\
x - y &= -2
\end{aligned}\

- one solution at $(3, -1)$
- no solutions
- one solution at $(3, 5)$
- infinitely many solutions

Question

determine how many solutions the system has. if it has one solution, state what the solution is.

\\begin{aligned}
2x - 3y &= -9 \\
x - y &= -2
\end{aligned}\

- one solution at $(3, -1)$
- no solutions
- one solution at $(3, 5)$
- infinitely many solutions

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", "Substitution Method" ], "new_concepts": [], "current_concepts": [ "Systems of Linear Equations", "Substitution Method" ] } ## Express x in terms of y $$ \begin{aligned} x - y &= -2 \ x &= y - 2 \end{aligned} $$ ## Substitute into the first equation $$ \begin{aligned} 2(y - 2) - 3y &= -9 \ 2y - 4 - 3y &= -9 \ -y - 4 &= -9 \ -y &= -5 \ y &= 5 \end{aligned} $$ ## Solve for x $$ \begin{aligned} x &= 5 - 2 \ x &= 3 \end{aligned} $$

One solution at $(3, -1)$

No solutions

One solution at $(3, 5)$

Infinitely many solutions

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

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QUESTION IMAGE

Question

Explanation:

Express x in terms of y

Substitute into the first equation

Solve for x

Answer: