Solve the system of equations. y = x^2 + 18x + 5 y = x - 11 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Substitute y into first equation: Substitute y from the second equation into the first equation: x^2 + 18x + 5 = x - 11.Solve for x: Now, let's solve for x: x^2 + 18x + 5 - x + 11 = 0, which simplifies to x^2 + 17x + 16 = 0.Factor quadratic equation: Factor the quadratic equation: (x + 1)(x + 16) = 0.Set factors equal to zero: Set each factor equal to zero and solve for x: x + 1 = 0 or x + 16 = 0.Solve for x: Solving x + 1 = 0 gives us x = -1.Find y for x = -1: Solving x + 16 = 0 gives us x = -16.Find y for x = -16: Substitute x = -1 into the second equation to find y: y = -1 - 11, so y = -12.Substitute x = -16 into the second equation to find y: y = -16 - 11, so y = -27.

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Solve the system of equations. $\newline$ $y = x^2 + 18x + 5$ $\newline$ $y = x - 11$ $\newline$ 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 + 18x + 5

\newline

y = x - 11

\newline

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

\newline

(______,______)

\newline

(______,______)

Substitute $y$ into first equation: Substitute $y$ from the second equation into the first equation: $x^2 + 18x + 5 = x - 11$ .
Solve for x: Now, let's solve for x: $x^2 + 18x + 5 - x + 11 = 0$ , which simplifies to $x^2 + 17x + 16 = 0$ .
Factor quadratic equation: Factor the quadratic equation: $(x + 1)(x + 16) = 0$ .
Set factors equal to zero: Set each factor equal to zero and solve for $x$ : $x + 1 = 0$ or $x + 16 = 0$ .
Solve for x: Solving $x + 1 = 0$ gives us $x = -1$ .
Find $y$ for $x = -1$ : Solving $x + 16 = 0$ gives us $x = -16$ .
Find $y$ for $x = -16$ : Substitute $x = -1$ into the second equation to find $y$ : $y = -1 - 11$ , so $y = -12$ .
Find $y$ for $x = -16$ : Substitute $x = -1$ into the second equation to find $y$ : $y = -1 - 11$ , so $y = -12$ .Substitute $x = -16$ into the second equation to find $y$ : $y = -16 - 11$ , so $y = -27$ .