Solve the system of equations. y = x^2 - 5x + 30 y = -24x - 18 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. x^2 - 5x + 30 = -24x - 18Move Terms to One Side: Move all terms to one side to set the equation to zero. x^2 - 5x + 24x + 30 + 18 = 0 x^2 + 19x + 48 = 0Factor Quadratic Equation: Factor the quadratic equation. (x + 3)(x + 16) = 0Solve for x: Set each factor equal to zero and solve for x. x + 3 = 0 or x + 16 = 0 x = -3 or x = -16Substitute x Values: Substitute x values into one of the original equations to find y values. For x = -3: y = -24(-3) - 18 which gives y = 72 - 18 so y = 54. For x = -16: y = -24(-16) - 18 which gives y = 384 - 18 so y = 366.Write Coordinates: Write the coordinates in exact form. First Coordinate: (-3, 54) Second Coordinate: (-16, 366)

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Solve the system of equations. $\newline$ $y = x^2 - 5x + 30$ $\newline$ $y = -24x - 18$ $\newline$ 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 - 5x + 30

\newline

y = -24x - 18

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $x^2 - 5x + 30 = -24x - 18$
Move Terms to One Side: Move all terms to one side to set the equation to zero. $\newline$ $x^2 - 5x + 24x + 30 + 18 = 0$ $\newline$ $x^2 + 19x + 48 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x + 3)(x + 16) = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $x + 3 = 0$ or $x + 16 = 0$ $\newline$ $x = -3$ or $x = -16$
Substitute x Values: Substitute $x$ values into one of the original equations to find $y$ values. $\newline$ For $x = -3$ : $y = -24(-3) - 18$ which gives $y = 72 - 18$ so $y = 54$ . $\newline$ For $x = -16$ : $y = -24(-16) - 18$ which gives $y = 384 - 18$ so $y = 366$ .
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(-3, 54)$ $\newline$ Second Coordinate: $(-16, 366)$