Solve the system of equations. y = -46x + 41 y = x^2 - 46x - 40 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. -46x + 41 = x^2 - 46x - 40Move Terms to One Side: Move all terms to one side to set the equation to zero. x^2 - 46x + 46x - 40 - 41 = 0 x^2 - 81 = 0Factor Quadratic Equation: Factor the quadratic equation. (x - 9)(x + 9) = 0Solve for x: Solve for x by setting each factor equal to zero. x - 9 = 0 or x + 9 = 0 x = 9 or x = -9Substitute x = 9: Substitute x = 9 into one of the original equations to find y. y = -46(9) + 41 y = -414 + 41 y = -373Substitute x = -9: Substitute x = -9 into the same original equation to find the other y. y = -46(-9) + 41 y = 414 + 41 y = 455

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Solve the system of equations. $\newline$ $y = -46x + 41$ $\newline$ $y = x^2 - 46x - 40$ $\newline$ 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 = -46x + 41

\newline

y = x^2 - 46x - 40

\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 $y$ . $-46x + 41 = x^2 - 46x - 40$
Move Terms to One Side: Move all terms to one side to set the equation to zero. $\newline$ $x^2 - 46x + 46x - 40 - 41 = 0$ $\newline$ $x^2 - 81 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x - 9)(x + 9) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x - 9 = 0$ or $x + 9 = 0$ $\newline$ $x = 9$ or $x = -9$
Substitute $x = 9$ : Substitute $x = 9$ into one of the original equations to find $y$ . $\newline$ $y = -46(9) + 41$ $\newline$ $y = -414 + 41$ $\newline$ $y = -373$
Substitute $x = -9$ : Substitute $x = -9$ into the same original equation to find the other $y$ . $y = -46(-9) + 41$ $y = 414 + 41$ $y = 455$