Solve the system of equations. y = x^2 + 17x - 1 y = -7x - 24 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Set the two equations equal to each other to find the x-values where the graphs intersect. y = x^2 + 17x - 1 y = -7x - 24 x^2 + 17x - 1 = -7x - 24Move and Form Quadratic Equation: Move all terms to one side to form a quadratic equation. x^2 + 17x - 1 + 7x + 24 = 0 x^2 + 24x + 23 = 0Factor Quadratic Equation: Factor the quadratic equation. x^2 + 24x + 23 = 0 The factors of 23 that add up to 24 are 1 and 23. (x + 1)(x + 23) = 0Solve for x: Solve for x by setting each factor equal to zero. (x + 1) = 0 or (x + 23) = 0 x = -1 or x = -23Substitute and Find y: Substitute the x-values back into one of the original equations to find the corresponding y-values. For x = -1: y = -7(-1) - 24 y = 7 - 24 y = -17 For x = -23: y = -7(-23) - 24 y = 161 - 24 y = 137Write Coordinates: Write the coordinates in exact form. The coordinates of the intersection points are (-1, -17) and (-23, 137).

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Solve the system of equations. $\newline$ $y = x^2 + 17x - 1$ $\newline$ $y = -7x - 24$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Algebra 2

Solve a system of linear and quadratic equations: parabolas

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Q. Solve the system of equations.

\newline

y = x^2 + 17x - 1

\newline

y = -7x - 24

\newline

Write the coordinates in exact form. Simplify all fractions and radicals.

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other to find the $x$ -values where the graphs intersect. $\newline$ $y = x^2 + 17x - 1$ $\newline$ $y = -7x - 24$ $\newline$ $x^2 + 17x - 1 = -7x - 24$
Move and Form Quadratic Equation: Move all terms to one side to form a quadratic equation. $\newline$ $x^2 + 17x - 1 + 7x + 24 = 0$ $\newline$ $x^2 + 24x + 23 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $x^2 + 24x + 23 = 0$ $\newline$ The factors of $23$ that add up to $24$ are $1$ and $23$ . $\newline$ $(x + 1)(x + 23) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $(x + 1) = 0$ or $(x + 23) = 0$ $\newline$ $x = -1$ or $x = -23$
Substitute and Find $y$ : Substitute the $x$ -values back into one of the original equations to find the corresponding $y$ -values. $\newline$ For $x = -1$ : $\newline$ $y = -7(-1) - 24$ $\newline$ $y = 7 - 24$ $\newline$ $y = -17$ $\newline$ For $x = -23$ : $\newline$ $y = -7(-23) - 24$ $\newline$ $y = 161 - 24$ $\newline$ $x$ $0$
Write Coordinates: Write the coordinates in exact form. $\newline$ The coordinates of the intersection points are $(-1, -17)$ and $(-23, 137)$ .