Solve the system of equations. y = -13x + 81 y = x^2 - 13x - 40 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. -13x + 81 = x^2 - 13x - 40Move Terms, Set to Zero: Move all terms to one side to set the equation to zero. 0 = x^2 - 13x + 13x - 40 - 81Simplify Equation: Simplify the equation by combining like terms. 0 = x^2 - 121Factor Quadratic: Factor the quadratic equation. 0 = (x - 11)(x + 11)Solve for x: Set each factor equal to zero and solve for x. x - 11 = 0 or x + 11 = 0 x = 11 or x = -11Find y (x=11): Substitute x = 11 into one of the original equations to find y. y = -13(11) + 81 y = -143 + 81 y = -62Find y (x=-11): Substitute x = -11 into the same original equation to find the other y. y = -13(-11) + 81 y = 143 + 81 y = 224Write Coordinates: Write the coordinates in exact form. First Coordinate: (11, -62) Second Coordinate: (-11, 224)

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Solve the system of equations. $\newline$ $y = -13x + 81$ $\newline$ $y = x^2 - 13x - 40$ $\newline$ $\newline$ 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

Full solution

Q. Solve the system of equations.

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y = -13x + 81

\newline

y = x^2 - 13x - 40

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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 $y$ . $-13x + 81 = x^2 - 13x - 40$
Move Terms, Set to Zero: Move all terms to one side to set the equation to zero. $\newline$ $0 = x^2 - 13x + 13x - 40 - 81$
Simplify Equation: Simplify the equation by combining like terms. $\newline$ $0 = x^2 - 121$
Factor Quadratic: Factor the quadratic equation. $\newline$ $0 = (x - 11)(x + 11)$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $x - 11 = 0$ or $x + 11 = 0$ $\newline$ $x = 11$ or $x = -11$
Find $y$ ( $x=11$ ): Substitute $x = 11$ into one of the original equations to find $y$ .
$y = -13(11) + 81$
$y = -143 + 81$
$y = -62$
Find $y$ ( $x=-11$ ): Substitute $x = -11$ into the same original equation to find the other $y$ .
$y = -13(-11) + 81$
$y = 143 + 81$
$y = 224$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(11, -62)$ $\newline$ Second Coordinate: $(-11, 224)$