Solve the system of equations. y = x^2 - 2x - 5 y = -2x + 44 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = x^2 - 2x - 5 y = -2x + 44 To find the intersection points, we set the two equations equal to each other. x^2 - 2x - 5 = -2x + 44Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a standard quadratic equation. x^2 - 2x - 5 + 2x - 44 = 0 x^2 - 49 = 0Solve for x: Solve the quadratic equation for x. x^2 = 49 Take the square root of both sides. x = ±√49 x = ±7Find y-values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. Let's use y = -2x + 44. First, for x = 7: y = -2(7) + 44 y = -14 + 44 y = 30 Second, for x = -7: y = -2(-7) + 44 y = 14 + 44 y = 58Write Coordinates: Write the coordinates in exact form. The first coordinate is (7, 30). The second coordinate is (-7, 58).

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Solve the system of equations. $\newline$ $y = x^2 - 2x - 5$ $\newline$ $y = -2x + 44$ $\newline$ 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 = x^2 - 2x - 5

\newline

y = -2x + 44

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = x^2 - 2x - 5$ $\newline$ $y = -2x + 44$ $\newline$ To find the intersection points, we set the two equations equal to each other. $\newline$ $x^2 - 2x - 5 = -2x + 44$
Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a standard quadratic equation. $\newline$ $x^2 - 2x - 5 + 2x - 44 = 0$ $\newline$ $x^2 - 49 = 0$
Solve for x: Solve the quadratic equation for x. $\newline$ $x^2 = 49$ $\newline$ Take the square root of both sides. $\newline$ $x = \pm\sqrt{49}$ $\newline$ $x = \pm7$
Find y-values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. Let's use $y = -2x + 44$ . $\newline$ First, for $x = 7$ : $\newline$ $y = -2(7) + 44$ $\newline$ $y = -14 + 44$ $\newline$ $y = 30$ $\newline$ Second, for $x = -7$ : $\newline$ $y = -2(-7) + 44$ $\newline$ $y = 14 + 44$ $\newline$ $y = 58$
Write Coordinates: Write the coordinates in exact form. $\newline$ The first coordinate is $(7, 30)$ . $\newline$ The second coordinate is $(-7, 58)$ .