Solve the system of equations. y = x^2 - 2x - 2 y = -3x + 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 - 2x - 2 = -3x + 18Move Terms, Set to Zero: Move all terms to one side to set the equation to zero. x^2 - 2x + 3x - 2 - 18 = 0 x^2 + x - 20 = 0Factor Quadratic Equation: Factor the quadratic equation. (x + 5)(x - 4) = 0Solve for x: Set each factor equal to zero and solve for x. x + 5 = 0 or x - 4 = 0 x = -5 or x = 4Substitute x, Find y: Substitute x = -5 into the second equation to find y. y = -3(-5) + 18 y = 15 + 18 y = 33Write Coordinates: Substitute x = 4 into the second equation to find y. y = -3(4) + 18 y = -12 + 18 y = 6Write the coordinates in exact form. First Coordinate: (-5, 33) Second Coordinate: (4, 6)

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Solve the system of equations. $\newline$ $y = x^2 - 2x - 2$ $\newline$ $y = -3x + 18$ $\newline$ 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 - 2x - 2

\newline

y = -3x + 18

\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 since they both equal $y$ . $x^2 - 2x - 2 = -3x + 18$
Move Terms, Set to Zero: Move all terms to one side to set the equation to zero. $\newline$ $x^2 - 2x + 3x - 2 - 18 = 0$ $\newline$ $x^2 + x - 20 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x + 5)(x - 4) = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $x + 5 = 0$ or $x - 4 = 0$ $\newline$ $x = -5$ or $x = 4$
Substitute $x$ , Find $y$ : Substitute $x = -5$ into the second equation to find $y$ . $y = -3(-5) + 18$ $y = 15 + 18$ $y = 33$
Write Coordinates: Substitute $x = 4$ into the second equation to find $y$ . $\newline$ $y = -3(4) + 18$ $\newline$ $y = -12 + 18$ $\newline$ $y = $6$
Write Coordinates: Substitute $x = 4$ into the second equation to find $y$.$y = -3(4) + 18$$y = -12 + 18$$y = 6$Write the coordinates in exact form.First Coordinate: $(-5, 33)$Second Coordinate: $(4, 6)$