what is one of the solutions to the following system?

$\begin{cases} y - 3 = x \\ x^2 - 6x + 13 = y \end{cases}$

$\bigcirc$ $(-5, 2)$
$\bigcirc$ $(-2, 1)$
$\bigcirc$ $(2, 5)$
$\bigcirc$ $(8, 5)$

Question

what is one of the solutions to the following system?

$\begin{cases} y - 3 = x \\ x^2 - 6x + 13 = y \end{cases}$

$\bigcirc$ $(-5, 2)$
$\bigcirc$ $(-2, 1)$
$\bigcirc$ $(2, 5)$
$\bigcirc$ $(8, 5)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "System of Quadratic and Linear Equations", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "System of Quadratic and Linear Equations", "Solving Quadratic Equations" ] } ## Express y in terms of x $$ \begin{aligned} &y - 3 = x \ &y = x + 3 \end{aligned} $$ ## Substitute and set up the quadratic equation $$ \begin{aligned} &x^2 - 6x + 13 = x + 3 \ &x^2 - 7x + 10 = 0 \end{aligned} $$ ## Solve for x and find corresponding y values $$ \begin{aligned} &(x - 2)(x - 5) = 0 \ &x = 2 \implies y = 2 + 3 = 5 \implies (2, 5) \ &x = 5 \implies y = 5 + 3 = 8 \implies (5, 8) \end{aligned} $$

(-5, 2)

(-2, 1)

(2, 5)

(8, 5)

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

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Question

Explanation:

Express y in terms of x

Substitute and set up the quadratic equation

Solve for x and find corresponding y values

Answer: