Solve the system of equations. y = x^2 - 38x - 50 y = -38x + 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 - 38x - 50 y = -38x + 50 x^2 - 38x - 50 = -38x + 50Cancel Out Terms: Cancel out the -38x on both sides. x^2 - 38x - 50 + 38x = -38x + 50 + 38x 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 = -10Substitute x for y: Substitute x back into one of the original equations to find y. For x = 10: y = -38(10) + 50 y = -380 + 50 y = -330Substitute x Again: Substitute x back into one of the original equations to find y for the second value of x. For x = -10: y = -38(-10) + 50 y = 380 + 50 y = 430Write Coordinates: Write the coordinates in exact form. First Coordinate: (10, -330) Second Coordinate: (-10, 430)

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Solve the system of equations. $\newline$ $y = x^2 - 38x - 50$ $\newline$ $y = -38x + 50$ $\newline$ 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.

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y = x^2 - 38x - 50

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y = -38x + 50

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

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(______,______)

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(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $y = x^2 - 38x - 50$ $y = -38x + 50$ $x^2 - 38x - 50 = -38x + 50$
Cancel Out Terms: Cancel out the $-38x$ on both sides. $\newline$ $x^2 - 38x - 50 + 38x = -38x + 50 + 38x$ $\newline$ $x^2 - 50 = 50$
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 $x$ . $\sqrt{x^2} = \sqrt{100}$ $x = 10 \text{ or } x = -10$
Substitute $x$ for $y$ : Substitute $x$ back into one of the original equations to find $y$ . $\newline$ For $x = 10$ : $y = -38(10) + 50$ $\newline$ $y = -380 + 50$ $\newline$ $y = -330$
Substitute $x$ Again: Substitute $x$ back into one of the original equations to find $y$ for the second value of $x$ . $\newline$ For $x = -10$ : $y = -38(-10) + 50$ $\newline$ $y = 380 + 50$ $\newline$ $y = 430$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(10, -330)$ $\newline$ Second Coordinate: $(-10, 430)$