Solve the system of equations. y = -36x - 19 y = x^2 - 11x + 27 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 = -36x - 19 y = x^2 - 11x + 27 So, x^2 - 11x + 27 = -36x - 19Rearrange and Combine Terms: Rearrange the equation to set it to zero and combine like terms. x^2 - 11x + 27 + 36x + 19 = 0 x^2 + 25x + 46 = 0Factor Quadratic Equation: Factor the quadratic equation. (x + 2)(x + 23) = 0Solve for x: Solve for x by setting each factor equal to zero. x + 2 = 0 or x + 23 = 0 x = -2 or x = -23Substitute x Values: Substitute x = -2 into one of the original equations to find the corresponding y value. y = -36(-2) - 19 y = 72 - 19 y = 53Find Corresponding y Values: Substitute x = -23 into one of the original equations to find the corresponding y value. y = -36(-23) - 19 y = 828 - 19 y = 809

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Solve the system of equations. $\newline$ $y = -36x - 19$ $\newline$ $y = x^2 - 11x + 27$ $\newline$ 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 = -36x - 19

\newline

y = x^2 - 11x + 27

\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 $y$ . $y = -36x - 19$ $y = x^2 - 11x + 27$ So, $x^2 - 11x + 27 = -36x - 19$
Rearrange and Combine Terms: Rearrange the equation to set it to zero and combine like terms. $\newline$ $x^2 - 11x + 27 + 36x + 19 = 0$ $\newline$ $x^2 + 25x + 46 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $(x + 2)(x + 23) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $x + 2 = 0$ or $x + 23 = 0$ $\newline$ $x = -2$ or $x = -23$
Substitute x Values: Substitute $x = -2$ into one of the original equations to find the corresponding $y$ value. $\newline$ $y = -36(-2) - 19$ $\newline$ $y = 72 - 19$ $\newline$ $y = 53$
Find Corresponding y Values: Substitute $x = -23$ into one of the original equations to find the corresponding y value. $\newline$ $y = -36(-23) - 19$ $\newline$ $y = 828 - 19$ $\newline$ $y = 809$