Solve the system of equations. y = x^2 - 24x - 30 y = -21x - 12 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal y. y = x^2 - 24x - 30 y = -21x - 12 x^2 - 24x - 30 = -21x - 12Form Quadratic Equation: Move all terms to one side to form a quadratic equation. x^2 - 24x - 30 + 21x + 12 = 0 x^2 - 3x - 18 = 0Factor Quadratic: Factor the quadratic equation. (x - 6)(x + 3) = 0Solve for x: Solve for x by setting each factor equal to zero. x - 6 = 0 or x + 3 = 0 x = 6 or x = -3Substitute and Find y: Substitute x values into the second equation to find corresponding y values. For x = 6: y = -21(6) - 12 which gives y = -126 - 12 so y = -138. For x = -3: y = -21(-3) - 12 which gives y = 63 - 12 so y = 51.Write Coordinates: Write the coordinates in exact form. First Coordinate: (6, -138) Second Coordinate: (-3, 51)

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Solve the system of equations. $\newline$ $y = x^2 - 24x - 30$ $\newline$ $y = -21x - 12$ $\newline$ 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 - 24x - 30

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y = -21x - 12

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

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(______,______)

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(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $y = x^2 - 24x - 30$ $y = -21x - 12$ $x^2 - 24x - 30 = -21x - 12$
Form Quadratic Equation: Move all terms to one side to form a quadratic equation. $\newline$ $x^2 - 24x - 30 + 21x + 12 = 0$ $\newline$ $x^2 - 3x - 18 = 0$
Factor Quadratic: Factor the quadratic equation. $\newline$ $(x - 6)(x + 3) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x - 6 = 0$ or $x + 3 = 0$ $\newline$ $x = 6$ or $x = -3$
Substitute and Find $y$ : Substitute $x$ values into the second equation to find corresponding $y$ values. $\newline$ For $x = 6$ : $y = -21(6) - 12$ which gives $y = -126 - 12$ so $y = -138$ . $\newline$ For $x = -3$ : $y = -21(-3) - 12$ which gives $y = 63 - 12$ so $x$ $0$ .
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(6, -138)$ $\newline$ Second Coordinate: $(-3, 51)$