type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.

consider this system of equations.
\\begin{cases} y = x^2 - 2x - 19 \\ y + 4x = 5 \end{cases}\

the points representing the solution set of this system of equations are (-6, 29) and ( , ).

Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.

consider this system of equations.
\\begin{cases} y = x^2 - 2x - 19 \\ y + 4x = 5 \end{cases}\

the points representing the solution set of this system of equations are (-6, 29) and (  ,   ).

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear-Quadratic Systems", "Quadratic Formula Application" ], "new_concepts": [], "current_concepts": [ "Linear-Quadratic Systems", "Quadratic Formula Application", "Algebraic Rearrangement" ] } ## Equate the expressions for y $$ \begin{aligned} &y = x^2 - 2x - 19\ &y = -4x + 5\ &x^2 - 2x - 19 = -4x + 5 \end{aligned} $$ ## Solve the quadratic equation $$ \begin{aligned} &x^2 + 2x - 24 = 0\ &(x + 6)(x - 4) = 0\ &x = -6 \quad \text{or} \quad x = 4 \end{aligned} $$ ## Find the corresponding y-value $$ \begin{aligned} &\text{For } x = 4:\ &y = -4(4) + 5 = -11 \end{aligned} $$ Consider this system of equations. $$ \begin{aligned} y &= x^2 - 2x - 19\ y + 4x &= 5 \end{aligned} $$ The points representing the solution set of this system of equations are $(-6, 29)$ and (4, -11). { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Linear-Quadratic Systems" ] }

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QUESTION IMAGE

Question

Explanation:

Equate the expressions for y

Solve the quadratic equation

Find the corresponding y-value

Answer: