Solve the system of equations. y = x^2 - 21x - 50 y = -21x + 50 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. y = x^2 - 21x - 50 y = -21x + 50 x^2 - 21x - 50 = -21x + 50Cancel Out Terms: Cancel out the -21x on both sides. x^2 - 21x - 50 + 21x = -21x + 50 + 21x x^2 - 50 = 50Add to Isolate x^2: Add 50 to both sides to isolate x^2. x^2 - 50 + 50 = 50 + 50 x^2 = 100Take Square Root: Take the square root of both sides to solve for x. sqrt(x^2) = sqrt(100) x = 10 or x = -10Plug x = 10: Plug x = 10 into the second equation to find y. y = -21(10) + 50 y = -210 + 50 y = -160Plug x = -10: Plug x = -10 into the second equation to find y. y = -21(-10) + 50 y = 210 + 50 y = 260Write Coordinates: Write the coordinates in exact form. First Coordinate: (10, -160) Second Coordinate: (-10, 260)

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Solve the system of equations. $\newline$ $y = x^2 - 21x - 50$ $\newline$ $y = -21x + 50$ $\newline$ 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 - 21x - 50

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y = -21x + 50

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

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(______,______)

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $y = x^2 - 21x - 50$ $y = -21x + 50$ $x^2 - 21x - 50 = -21x + 50$
Cancel Out Terms: Cancel out the $-21x$ on both sides. $\newline$ $x^2 - 21x - 50 + 21x = -21x + 50 + 21x$ $\newline$ $x^2 - 50 = 50$
Add to Isolate $x^2$ : Add $50$ to both sides to isolate $x^2$ . $\newline$ $x^2 - 50 + 50 = 50 + 50$ $\newline$ $x^2 = 100$
Take Square Root: Take the square root of both sides to solve for $x$ . $\sqrt{x^2} = \sqrt{100}$ $x = 10 \text{ or } x = -10$
Plug $x = 10$ : Plug $x = 10$ into the second equation to find $y$ . $y = -21(10) + 50$ $y = -210 + 50$ $y = -160$
Plug $x = -10$ : Plug $x = -10$ into the second equation to find $y$ . $\newline$ $y = -21(-10) + 50$ $\newline$ $y = 210 + 50$ $\newline$ $y = 260$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(10, -160)$ $\newline$ Second Coordinate: $(-10, 260)$