select the correct answer.

how many real solutions exist for this system of equations?

$y = x^2 + 4$

$y = 4x$

- zero
- one
- two
- infinite

Question

select the correct answer.

how many real solutions exist for this system of equations?

$y = x^2 + 4$

$y = 4x$

- zero
- one
- two
- infinite

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear-Quadratic Systems", "Quadratic Formula Application" ], "new_concepts": [], "current_concepts": [ "Linear-Quadratic Systems", "Quadratic Equations", "Discriminant" ] } ## Equate the two equations to find intersection points $$ x^2 + 4 = 4x $$ ## Rearrange into standard quadratic form $$ x^2 - 4x + 4 = 0 $$ ## Calculate the discriminant or factor the equation $$ \begin{aligned} &(x - 2)^2 = 0 \ &x = 2 \ &D = (-4)^2 - 4(1)(4) = 16 - 16 = 0 \end{aligned} $$

zero one

two

infinite

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

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QUESTION IMAGE

Question

Explanation:

Equate the two equations to find intersection points

Rearrange into standard quadratic form

Calculate the discriminant or factor the equation

Answer: