Solve the system of equations. y = x^2 - 22x + 9 y = -x - 29 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. y = x^2 - 22x + 9 y = -x - 29 So, x^2 - 22x + 9 = -x - 29Move and Simplify: Move all terms to one side to set the equation to zero and simplify. x^2 - 22x + x + 9 + 29 = 0 x^2 - 21x + 38 = 0Factor Quadratic Equation: Factor the quadratic equation. (x - 19)(x - 2) = 0Solve for x: Solve for x by setting each factor equal to zero. x - 19 = 0 or x - 2 = 0 So, x = 19 or x = 2Substitute x = 19: Substitute x = 19 into one of the original equations to find the corresponding y value. Using y = -x - 29: y = -(19) - 29 y = -19 - 29 y = -48Substitute x = 2: Substitute x = 2 into one of the original equations to find the corresponding y value. Using y = -x - 29: y = -(2) - 29 y = -2 - 29 y = -31

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Solve the system of equations. $\newline$ $y = x^2 - 22x + 9$ $\newline$ $y = -x - 29$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Algebra 2

Solve a nonlinear system of equations

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Q. Solve the system of equations.

\newline

y = x^2 - 22x + 9

\newline

y = -x - 29

\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 $y$ . $y = x^2 - 22x + 9$ $y = -x - 29$ So, $x^2 - 22x + 9 = -x - 29$
Move and Simplify: Move all terms to one side to set the equation to zero and simplify. $\newline$ $x^2 - 22x + x + 9 + 29 = 0$ $\newline$ $x^2 - 21x + 38 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x - 19)(x - 2) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x - 19 = 0$ or $x - 2 = 0$ $\newline$ So, $x = 19$ or $x = 2$
Substitute $x = 19$ : Substitute $x = 19$ into one of the original equations to find the corresponding $y$ value. $\newline$ Using $y = -x - 29$ : $\newline$ $y = -(19) - 29$ $\newline$ $y = -19 - 29$ $\newline$ $y = -48$
Substitute $x = 2$ : Substitute $x = 2$ into one of the original equations to find the corresponding $y$ value. $\newline$ Using $y = -x - 29$ : $\newline$ $y = -(2) - 29$ $\newline$ $y = -2 - 29$ $\newline$ $y = -31$