Solve the system of equations. y = -34x + 75 y = x^2 - 34x - 46 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the following system of equations: y = -34x + 75 y = x^2 - 34x - 46 Set the two equations equal to each other to find the x-values where their y-values are the same. -34x + 75 = x^2 - 34x - 46Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. 0 = x^2 - 34x - 46 + 34x - 75 0 = x^2 - 121Solve for x: Solve the quadratic equation for x. x^2 = 121 Take the square root of both sides. x = ±11Find Corresponding y-values: Find the corresponding y-values for each x-value by substituting back into either of the original equations. Let's use y = -34x + 75. For x = 11: y = -34(11) + 75 y = -374 + 75 y = -299 For x = -11: y = -34(-11) + 75 y = 374 + 75 y = 449Write Coordinates: Write the coordinates in exact form. The solutions to the system of equations are the points where the two graphs intersect, which are the x-values we found and their corresponding y-values. First Coordinate: (11, -299) Second Coordinate: (-11, 449)

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Solve the system of equations. $\newline$ $y = -34x + 75$ $\newline$ $y = x^2 - 34x - 46$ $\newline$ 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 = -34x + 75

\newline

y = x^2 - 34x - 46

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the following system of equations: $\newline$ $y = -34x + 75$ $\newline$ $y = x^2 - 34x - 46$ $\newline$ Set the two equations equal to each other to find the $x$ -values where their $y$ -values are the same. $\newline$ $-34x + 75 = x^2 - 34x - 46$
Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. $\newline$ $0 = x^2 - 34x - 46 + 34x - 75$ $\newline$ $0 = x^2 - 121$
Solve for x: Solve the quadratic equation for x. $\newline$ $x^2 = 121$ $\newline$ Take the square root of both sides. $\newline$ $x = \pm11$
Find Corresponding y-values: Find the corresponding y-values for each $x$ -value by substituting back into either of the original equations. Let's use $y = -34x + 75$ . For $x = 11$ : $y = -34(11) + 75$ $y = -374 + 75$ $y = -299$ For $x = -11$ : $y = -34(-11) + 75$ $y = 374 + 75$ $y = 449$
Write Coordinates: Write the coordinates in exact form. $\newline$ The solutions to the system of equations are the points where the two graphs intersect, which are the $x$ -values we found and their corresponding $y$ -values. $\newline$ First Coordinate: $(11, -299)$ $\newline$ Second Coordinate: $(-11, 449)$