Solve the system of equations. y = -8x + 50 y = x^2 - 8x - 50 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = -8x + 50 y = x^2 - 8x - 50 Set the two equations equal to each other to find the x-values where their y-values are the same. -8x + 50 = x^2 - 8x - 50Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. 0 = x^2 - 8x - 50 + 8x - 50 0 = x^2 - 100Solve for x: Solve the quadratic equation for x. x^2 = 100 Take the square root of both sides. x = ±sqrt(100) x = ±10Find y-values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. Let's use y = -8x + 50. For x = 10: y = -8(10) + 50 y = -80 + 50 y = -30Find y for x=-10: Find the y-value for x = -10: y = -8(-10) + 50 y = 80 + 50 y = 130Write Coordinates: Write the coordinates in exact form. First Coordinate: (10, -30) Second Coordinate: (-10, 130)

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Solve the system of equations. $\newline$ $y = -8x + 50$ $\newline$ $y = x^2 - 8x - 50$ $\newline$ 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 = -8x + 50

\newline

y = x^2 - 8x - 50

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = -8x + 50$ $\newline$ $y = x^2 - 8x - 50$ $\newline$ Set the two equations equal to each other to find the $x$ -values where their $y$ -values are the same. $\newline$ $-8x + 50 = x^2 - 8x - 50$
Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. $\newline$ $0 = x^2 - 8x - 50 + 8x - 50$ $\newline$ $0 = x^2 - 100$
Solve for x: Solve the quadratic equation for x. $\newline$ $x^2 = 100$ $\newline$ Take the square root of both sides. $\newline$ $x = \pm\sqrt{100}$ $\newline$ $x = \pm10$
Find y-values: Find the corresponding y-values for each $x$ -value by substituting back into one of the original equations. Let's use $y = -8x + 50$ . $\newline$ For $x = 10$ : $\newline$ $y = -8(10) + 50$ $\newline$ $y = -80 + 50$ $\newline$ $y = -30$
Find $y$ for $x=-10$ : Find the $y$ -value for $x = -10$ : $y = -8(-10) + 50$ $y = 80 + 50$ $y = 130$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(10, -30)$ $\newline$ Second Coordinate: $(-10, 130)$