Solve the system of equations. y = x^2 - 31x - 30 y = -21x - 46 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 - 31x - 30 = -21x - 46Form Quadratic Equation: Move all terms to one side to form a quadratic equation. x^2 - 31x + 21x - 30 + 46 = 0 x^2 - 10x + 16 = 0Factor Quadratic: Factor the quadratic equation. (x - 8)(x - 2) = 0Solve for x: Solve for x by setting each factor equal to zero. x - 8 = 0 or x - 2 = 0 x = 8 or x = 2Substitute x for y: Substitute x = 8 into the second equation to find y. y = -21(8) - 46 y = -168 - 46 y = -214Find Coordinates: Substitute x = 2 into the second equation to find y. y = -21(2) - 46 y = -42 - 46 y = -88Write the coordinates in exact form. First Coordinate: (8, -214) Second Coordinate: (2, -88)

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Solve the system of equations. $\newline$ $y = x^2 - 31x - 30$ $\newline$ $y = -21x - 46$ $\newline$ 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 - 31x - 30

\newline

y = -21x - 46

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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 $y$ . $x^2 - 31x - 30 = -21x - 46$
Form Quadratic Equation: Move all terms to one side to form a quadratic equation. $\newline$ $x^2 - 31x + 21x - 30 + 46 = 0$ $\newline$ $x^2 - 10x + 16 = 0$
Factor Quadratic: Factor the quadratic equation. $\newline$ $(x - 8)(x - 2) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x - 8 = 0$ or $x - 2 = 0$ $\newline$ $x = 8$ or $x = 2$
Substitute $x$ for $y$ : Substitute $x = 8$ into the second equation to find $y$ . $\newline$ $y = -21(8) - 46$ $\newline$ $y = -168 - 46$ $\newline$ $y = -214$
Find Coordinates: Substitute $x = 2$ into the second equation to find $y$ . $y = -21(2) - 46$ $y = -42 - 46$ $y = -88$
Find Coordinates: Substitute $x = 2$ into the second equation to find $y$ . $y = -21(2) - 46$ $y = -42 - 46$ $y = -88$ Write the coordinates in exact form. $\newline$ First Coordinate: $(8, -214)$ $\newline$ Second Coordinate: $(2, -88)$