Solve the system of equations. y = -44x + 100 y = x^2 - 44x - 44 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = -44x + 100 y = x^2 - 44x - 44 Set the two equations equal to each other to find the x-values where they intersect. -44x + 100 = x^2 - 44x - 44Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. 0 = x^2 - 44x - 44 + 44x - 100 0 = x^2 - 144Solve for x: Solve the quadratic equation for x. x^2 = 144 Take the square root of both sides. x = ±12Find y-values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. Let's use y = -44x + 100. For x = 12: y = -44(12) + 100 y = -528 + 100 y = -428Find Second y-value: Find the y-value for the second x-value. For x = -12: y = -44(-12) + 100 y = 528 + 100 y = 628Write Coordinates: Write the coordinates in exact form. First Coordinate: (12, -428) Second Coordinate: (-12, 628)

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Solve the system of equations. $\newline$ $y = -44x + 100$ $\newline$ $y = x^2 - 44x - 44$ $\newline$ 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 = -44x + 100

\newline

y = x^2 - 44x - 44

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = -44x + 100$ $\newline$ $y = x^2 - 44x - 44$ $\newline$ Set the two equations equal to each other to find the $x$ -values where they intersect. $\newline$ $-44x + 100 = x^2 - 44x - 44$
Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. $\newline$ $0 = x^2 - 44x - 44 + 44x - 100$ $\newline$ $0 = x^2 - 144$
Solve for x: Solve the quadratic equation for x. $\newline$ $x^2 = 144$ $\newline$ Take the square root of both sides. $\newline$ $x = \pm12$
Find y-values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. Let's use $y = -44x + 100$ . $\newline$ For $x = 12$ : $\newline$ $y = -44(12) + 100$ $\newline$ $y = -528 + 100$ $\newline$ $y = -428$
Find Second y-value: Find the y-value for the second x-value. $\newline$ For $x = -12$ : $\newline$ $y = -44(-12) + 100$ $\newline$ $y = 528 + 100$ $\newline$ $y = 628$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(12, -428)$ $\newline$ Second Coordinate: $(-12, 628)$