Solve the system of equations. y = -47x + 45 y = x^2 - 47x - 19 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. -47x + 45 = x^2 - 47x - 19Move Terms, Set to Zero: Move all terms to one side to set the equation to zero. 0 = x^2 - 47x + 47x - 19 - 45Simplify Equation: Simplify the equation by combining like terms. 0 = x^2 - 64Factor Quadratic: Factor the quadratic equation. 0 = (x - 8)(x + 8)Solve for x: Set each factor equal to zero and solve for x. x - 8 = 0 and x + 8 = 0 x = 8 and x = -8Substitute x, Find y: Substitute x = 8 into one of the original equations to find y. y = -47(8) + 45 y = -376 + 45 y = -331Substitute x = -8, Find y: Substitute x = -8 into the same original equation to find y. y = -47(-8) + 45 y = 376 + 45 y = 421Write Coordinates: Write the coordinates in exact form. First Coordinate: (8, -331) Second Coordinate: (-8, 421)

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Solve the system of equations. $\newline$ $y = -47x + 45$ $\newline$ $y = x^2 - 47x - 19$ $\newline$ $\newline$ 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 = -47x + 45

\newline

y = x^2 - 47x - 19

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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 $y$ . $-47x + 45 = x^2 - 47x - 19$
Move Terms, Set to Zero: Move all terms to one side to set the equation to zero. $\newline$ $0 = x^2 - 47x + 47x - 19 - 45$
Simplify Equation: Simplify the equation by combining like terms. $\newline$ $0 = x^2 - 64$
Factor Quadratic: Factor the quadratic equation. $\newline$ $0 = (x - 8)(x + 8)$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $x - 8 = 0$ and $x + 8 = 0$ $\newline$ $x = 8$ and $x = -8$
Substitute $x$ , Find $y$ : Substitute $x = 8$ into one of the original equations to find $y$ . $y = -47(8) + 45$ $y = -376 + 45$ $y = -331$
Substitute $x = -8$ , Find $y$ : Substitute $x = -8$ into the same original equation to find $y$ . $\newline$ $y = -47(-8) + 45$ $\newline$ $y = 376 + 45$ $\newline$ $y = 421$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(8, -331)$ $\newline$ Second Coordinate: $(-8, 421)$