Solve the system of equations. y = -20x - 22 y = x^2 - 37x + 20 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal y. -20x - 22 = x^2 - 37x + 20Move Terms to One Side: Move all terms to one side to set the equation to zero. x^2 - 37x + 20 + 20x + 22 = 0 x^2 - 17x + 42 = 0Factor Quadratic Equation: Factor the quadratic equation. (x - 14)(x - 3) = 0Solve for x: Solve for x by setting each factor equal to zero. x - 14 = 0 or x - 3 = 0 x = 14 or x = 3Substitute x Values: Substitute x = 14 into one of the original equations to find y. y = -20(14) - 22 y = -280 - 22 y = -302Find y Values: Substitute x = 3 into one of the original equations to find y. y = -20(3) - 22 y = -60 - 22 y = -82Write Coordinates: Write the coordinates in exact form. First Coordinate: (14, -302) Second Coordinate: (3, -82)

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Solve the system of equations. $\newline$ $y = -20x - 22$ $\newline$ $y = x^2 - 37x + 20$ $\newline$ 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 = -20x - 22

\newline

y = x^2 - 37x + 20

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: Set the two equations equal to each other since they both equal $y$ . $-20x - 22 = x^2 - 37x + 20$
Move Terms to One Side: Move all terms to one side to set the equation to zero. $\newline$ $x^2 - 37x + 20 + 20x + 22 = 0$ $\newline$ $x^2 - 17x + 42 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x - 14)(x - 3) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x - 14 = 0$ or $x - 3 = 0$ $\newline$ $x = 14$ or $x = 3$
Substitute x Values: Substitute $x = 14$ into one of the original equations to find $y$ . $\newline$ $y = -20(14) - 22$ $\newline$ $y = -280 - 22$ $\newline$ $y = $-302$
Find y Values: Substitute $x = 3$ into one of the original equations to find $y$.$y = -20(3) - 22$$y = -60 - 22$$y = -82$
Write Coordinates: Write the coordinates in exact form.$\newline$First Coordinate: $(14, -302)$$\newline$Second Coordinate: $(3, -82)$