Solve the system of equations. y = -4x + 10 y = x^2 - 12x + 25 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. -4x + 10 = x^2 - 12x + 25Move Terms to One Side: Move all terms to one side to set the equation to zero. x^2 - 12x + 4x + 25 - 10 = 0 x^2 - 8x + 15 = 0Factor Quadratic Equation: Factor the quadratic equation. (x - 3)(x - 5) = 0Solve for x: Solve for x by setting each factor equal to zero. x - 3 = 0 or x - 5 = 0 x = 3 or x = 5Substitute x Values: Substitute x = 3 into one of the original equations to find y. y = -4(3) + 10 y = -12 + 10 y = -2Find y Values: Substitute x = 5 into the same original equation to find y. y = -4(5) + 10 y = -20 + 10 y = -10Write Coordinates: Write the coordinates in exact form. First Coordinate: (3, -2) Second Coordinate: (5, -10)

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Solve the system of equations. $\newline$ $y = -4x + 10$ $\newline$ $y = x^2 - 12x + 25$ $\newline$ 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 = -4x + 10

\newline

y = x^2 - 12x + 25

\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 $y$ . $-4x + 10 = x^2 - 12x + 25$
Move Terms to One Side: Move all terms to one side to set the equation to zero. $\newline$ $x^2 - 12x + 4x + 25 - 10 = 0$ $\newline$ $x^2 - 8x + 15 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x - 3)(x - 5) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x - 3 = 0$ or $x - 5 = 0$ $\newline$ $x = 3$ or $x = 5$
Substitute x Values: Substitute $x = 3$ into one of the original equations to find $y$ . $\newline$ $y = -4(3) + 10$ $\newline$ $y = -12 + 10$ $\newline$ $y = -2$
Find y Values: Substitute $x = 5$ into the same original equation to find y. $\newline$ $y = -4(5) + 10$ $\newline$ $y = -20 + 10$ $\newline$ $y = -10$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(3, -2)$ $\newline$ Second Coordinate: $(5, -10)$