Solve the system of equations. y = x^2 - 40x + 20 y = -21x - 28 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. x^2 - 40x + 20 = -21x - 28Move Terms to One Side: Move all terms to one side to set the equation to zero. x^2 - 40x + 21x + 20 + 28 = 0 x^2 - 19x + 48 = 0Factor Quadratic Equation: Factor the quadratic equation. (x - 16)(x - 3) = 0Solve for x: Solve for x by setting each factor equal to zero. x - 16 = 0 or x - 3 = 0 x = 16 or x = 3Substitute x into Second Equation: Substitute x = 16 into the second equation to find y. y = -21(16) - 28 y = -336 - 28 y = -364Find Coordinates: Substitute x = 3 into the second equation to find y. y = -21(3) - 28 y = -63 - 28 y = -91Write the coordinates in exact form. First Coordinate: (16, -364) Second Coordinate: (3, -91)

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Solve the system of equations. $\newline$ $y = x^2 - 40x + 20$ $\newline$ $y = -21x - 28$ $\newline$ 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 - 40x + 20

\newline

y = -21x - 28

\newline

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 $y$ . $x^2 - 40x + 20 = -21x - 28$
Move Terms to One Side: Move all terms to one side to set the equation to zero. $\newline$ $x^2 - 40x + 21x + 20 + 28 = 0$ $\newline$ $x^2 - 19x + 48 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x - 16)(x - 3) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x - 16 = 0$ or $x - 3 = 0$ $\newline$ $x = 16$ or $x = 3$
Substitute $x$ into Second Equation: Substitute $x = 16$ into the second equation to find $y$ . $\newline$ $y = -21(16) - 28$ $\newline$ $y = -336 - 28$ $\newline$ $y = -364$
Find Coordinates: Substitute $x = 3$ into the second equation to find $y$ . $\newline$ $y = -21(3) - 28$ $\newline$ $y = -63 - 28$ $\newline$ $y = $-91$
Find Coordinates: Substitute $x = 3$ into the second equation to find $y$.$\newline$$y = -21(3) - 28$$\newline$$y = -63 - 28$$\newline$$y = -91$Write the coordinates in exact form.$\newline$First Coordinate: $(16, -364)$$\newline$Second Coordinate: $(3, -91)$