Solve the system of equations. y = -14x + 75 y = x^2 - 14x - 46 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = -14x + 75 y = x^2 - 14x - 46 Set the two equations equal to each other to find the x-values where their y-values are the same. -14x + 75 = x^2 - 14x - 46Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. 0 = x^2 - 14x - 46 + 14x - 75 0 = x^2 - 121Solve Quadratic Equation: Solve the quadratic equation. x^2 = 121 Take the square root of both sides. x = ±11Substitute for Y-Values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. Let's use y = -14x + 75. For x = 11: y = -14(11) + 75 y = -154 + 75 y = -79Find Y-Value: Find the y-value for the second x-value. For x = -11: y = -14(-11) + 75 y = 154 + 75 y = 229Write Coordinates: Write the coordinates in exact form. The solutions to the system of equations are the points where the two graphs intersect. First Coordinate: (11, -79) Second Coordinate: (-11, 229)

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Solve the system of equations. $\newline$ $y = -14x + 75$ $\newline$ $y = x^2 - 14x - 46$ $\newline$ 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 = -14x + 75

\newline

y = x^2 - 14x - 46

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = -14x + 75$ $\newline$ $y = x^2 - 14x - 46$ $\newline$ Set the two equations equal to each other to find the $x$ -values where their $y$ -values are the same. $\newline$ $-14x + 75 = x^2 - 14x - 46$
Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. $\newline$ $0 = x^2 - 14x - 46 + 14x - 75$ $\newline$ $0 = x^2 - 121$
Solve Quadratic Equation: Solve the quadratic equation. $\newline$ $x^2 = 121$ $\newline$ Take the square root of both sides. $\newline$ $x = \pm11$
Substitute for Y-Values: Find the corresponding $y$ -values for each $x$ -value by substituting back into one of the original equations. Let's use $y = -14x + 75$ . For $x = 11$ : $y = -14(11) + 75$ $y = -154 + 75$ $y = -79$
Find Y-Value: Find the y-value for the second x-value. $\newline$ For $x = -11$ : $\newline$ $y = -14(-11) + 75$ $\newline$ $y = 154 + 75$ $\newline$ $y = 229$
Write Coordinates: Write the coordinates in exact form. $\newline$ The solutions to the system of equations are the points where the two graphs intersect. $\newline$ First Coordinate: $(11, -79)$ $\newline$ Second Coordinate: $(-11, 229)$