Solve the system of equations. y = -10x + 44 y = x^2 - 5x - 6 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. -10x + 44 = x^2 - 5x - 6Move Terms to One Side: Move all terms to one side to set the equation to zero. x^2 - 5x + 10x - 6 - 44 = 0 x^2 + 5x - 50 = 0Factor Quadratic Equation: Factor the quadratic equation. (x + 10)(x - 5) = 0Solve for x: Solve for x by setting each factor equal to zero. x + 10 = 0 or x - 5 = 0 x = -10 or x = 5Substitute x Values: Substitute x = -10 into one of the original equations to find y. y = -10(-10) + 44 y = 100 + 44 y = 144Write Coordinates: Substitute x = 5 into one of the original equations to find y. y = -10(5) + 44 y = -50 + 44 y = -6Write the coordinates in exact form. First Coordinate: (-10, 144) Second Coordinate: (5, -6)

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Solve the system of equations. $\newline$ $y = -10x + 44$ $\newline$ $y = x^2 - 5x - 6$ $\newline$ 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 = -10x + 44

\newline

y = x^2 - 5x - 6

\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 $y$ . $-10x + 44 = x^2 - 5x - 6$
Move Terms to One Side: Move all terms to one side to set the equation to zero. $\newline$ $x^2 - 5x + 10x - 6 - 44 = 0$ $\newline$ $x^2 + 5x - 50 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x + 10)(x - 5) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x + 10 = 0$ or $x - 5 = 0$ $\newline$ $x = -10$ or $x = 5$
Substitute x Values: Substitute $x = -10$ into one of the original equations to find $y$ . $y = -10(-10) + 44$ $y = 100 + 44$ $y = 144$
Write Coordinates: Substitute $x = 5$ into one of the original equations to find $y$ . $\newline$ $y = -10(5) + 44$ $\newline$ $y = -50 + 44$ $\newline$ $y = -6$
Write Coordinates: Substitute $x = 5$ into one of the original equations to find $y$ . $\newline$ $y = -10(5) + 44$ $\newline$ $y = -50 + 44$ $\newline$ $y = -6$ Write the coordinates in exact form. $\newline$ First Coordinate: $(-10, 144)$ $\newline$ Second Coordinate: $(5, -6)$