Solve the system of equations. y = -50x + 78 y = x^2 - 50x - 43 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = -50x + 78 y = x^2 - 50x - 43 Set the two equations equal to each other to find the x-values where they intersect. -50x + 78 = x^2 - 50x - 43Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. 0 = x^2 - 50x - 43 + 50x - 78 0 = x^2 - 121Factor Quadratic Equation: Factor the quadratic equation. 0 = (x - 11)(x + 11)Solve for x: Solve for x by setting each factor equal to zero. (x - 11) = 0 or (x + 11) = 0 x = 11 or x = -11Find Corresponding y-values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. Let's use y = -50x + 78. For x = 11: y = -50(11) + 78 y = -550 + 78 y = -472 For x = -11: y = -50(-11) + 78 y = 550 + 78 y = 628Write Coordinates: Write the coordinates in exact form. First Coordinate: (11, -472) Second Coordinate: (-11, 628)

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Solve the system of equations. $\newline$ $y = -50x + 78$ $\newline$ $y = x^2 - 50x - 43$ $\newline$ 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 = -50x + 78

\newline

y = x^2 - 50x - 43

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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: $\newline$ $y = -50x + 78$ $\newline$ $y = x^2 - 50x - 43$ $\newline$ Set the two equations equal to each other to find the $x$ -values where they intersect. $\newline$ $-50x + 78 = x^2 - 50x - 43$
Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. $\newline$ $0 = x^2 - 50x - 43 + 50x - 78$ $\newline$ $0 = x^2 - 121$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $0 = (x - 11)(x + 11)$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $(x - 11) = 0$ or $(x + 11) = 0$ $\newline$ $x = 11$ or $x = -11$
Find Corresponding y-values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. Let's use $y = -50x + 78$ . $\newline$ For $x = 11$ : $\newline$ $y = -50(11) + 78$ $\newline$ $y = -550 + 78$ $\newline$ $y = -472$ $\newline$ For $x = -11$ : $\newline$ $y = -50(-11) + 78$ $\newline$ $y = 550 + 78$ $\newline$ $y = 628$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(11, -472)$ $\newline$ Second Coordinate: $(-11, 628)$