solve the system of equations shown.

\
\begin{aligned}
x+y&=9 \\
x&=4y-11
\end{aligned}
\

- none of these
- $(5, -4)$
- $(4, 5)$
- $(-5, 4)$

Question

solve the system of equations shown.

\
\begin{aligned}
x+y&=9 \\
x&=4y-11
\end{aligned}
\

- none of these
- $(5, -4)$
- $(4, 5)$
- $(-5, 4)$

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" ] } ## Substitute the expression for x into the first equation $$ \begin{aligned} &(4y - 11) + y = 9 \ &5y - 11 = 9 \ &5y = 20 \ &y = 4 \end{aligned} $$ ## Solve for x using the value of y $$ \begin{aligned} &x = 4(4) - 11 \ &x = 16 - 11 \ &x = 5 \end{aligned} $$ ## Verify the solution against the options $$ \begin{aligned} &(x, y) = (5, 4) \end{aligned} $$

None of these

(5, -4)

(4, 5)

(-5, 4)

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

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QUESTION IMAGE

Question

Explanation:

Substitute the expression for x into the first equation

Solve for x using the value of y

Verify the solution against the options

Answer: