Solve the system of equations. y = -18x + 47 y = x^2 - 18x - 34 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y Equation: Substitute y from the first equation into the second equation. This gives us -18x + 47 = x^2 - 18x - 34.Simplify Equation: Simplify the equation by moving all terms to one side to set the equation to zero: 0 = x^2 - 34 - 47.Combine Like Terms: Combine like terms to get the quadratic equation: 0 = x^2 - 81.Factor Quadratic Equation: Factor the quadratic equation: 0 = (x - 9)(x + 9).Solve for x: Solve for x by setting each factor equal to zero: x - 9 = 0 and x + 9 = 0.Find Solutions for x: Find the two solutions for x: x = 9 and x = -9.Substitute x = 9: Substitute x = 9 into the first equation to find the corresponding y value: y = -18(9) + 47.Calculate y for x = 9: Calculate the y value for x = 9: y = -162 + 47.Substitute x = -9: Simplify to find the y value: y = -115.Calculate y for x = -9: Substitute x = -9 into the first equation to find the corresponding y value: y = -18(-9) + 47.Write Coordinate Points: Calculate the y value for x = -9: y = 162 + 47.Simplify to find the y value: y = 209.Write the solutions as coordinate points: The coordinate points are (9, -115) and (-9, 209).

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Solve the system of equations. $\newline$ $y = -18x + 47$ $\newline$ $y = x^2 - 18x - 34$ $\newline$ 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 = -18x + 47

\newline

y = x^2 - 18x - 34

\newline

Write the coordinates in exact form. Simplify all fractions and radicals.

\newline

(______,______)

\newline

(______,______)

Substitute $y$ Equation: Substitute $y$ from the first equation into the second equation. This gives us $-18x + 47 = x^2 - 18x - 34$ .
Simplify Equation: Simplify the equation by moving all terms to one side to set the equation to zero: $0 = x^2 - 34 - 47$ .
Combine Like Terms: Combine like terms to get the quadratic equation: $0 = x^2 - 81$ .
Factor Quadratic Equation: Factor the quadratic equation: $0 = (x - 9)(x + 9)$ .
Solve for x: Solve for x by setting each factor equal to zero: $x - 9 = 0$ and $x + 9 = 0$ .
Find Solutions for x: Find the two solutions for $x$ : $x = 9$ and $x = -9$ .
Substitute $x = 9$ : Substitute $x = 9$ into the first equation to find the corresponding $y$ value: $y = -18(9) + 47$ .
Calculate $y$ for $x = 9$ : Calculate the $y$ value for $x = 9$ : $y = -162 + 47$ .
Substitute $x = -9$ : Simplify to find the $y$ value: $y = -115$ .
Calculate $y$ for $x = -9$ : Substitute $x = -9$ into the first equation to find the corresponding $y$ value: $y = -18(-9) + 47$ .
Write Coordinate Points: Calculate the $y$ value for $x = -9$ : $y = 162 + 47$ .
Write Coordinate Points: Calculate the $y$ value for $x = -9$ : $y = 162 + 47$ .Simplify to find the $y$ value: $y = 209$ .
Write Coordinate Points: Calculate the $y$ value for $x = -9$ : $y = 162 + 47$ . Simplify to find the $y$ value: $y = 209$ . Write the solutions as coordinate points: The coordinate points are $(9, -115)$ and $(-9, 209)$ .