Solve the system of equations. y = -14x - 31 y = x^2 - 27x + 9 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Move and Simplify: Now, let's move everything to one side to get a quadratic equation. x^2 - 27x + 14x + 9 + 31 = 0 x^2 - 13x + 40 = 0Factor Quadratic Equation: Next, we need to factor the quadratic equation. (x - 5)(x - 8) = 0Solve for x: Now, we solve for x by setting each factor equal to zero. x - 5 = 0 or x - 8 = 0 So, x = 5 or x = 8Find y-values: Let's find the corresponding y-values by plugging x back into one of the original equations. For x = 5, y = -14(5) - 31 which gives us y = -70 - 31 so y = -101.Find y-values: Now, for x = 8, y = -14(8) - 31 which gives us y = -112 - 31 so y = -143.Write Coordinates: Finally, we write the coordinates in exact form. The first coordinate is (5, -101) and the second coordinate is (8, -143).

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Solve the system of equations. $\newline$ $y = -14x - 31$ $\newline$ $y = x^2 - 27x + 9$ $\newline$ 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 = -14x - 31

\newline

y = x^2 - 27x + 9

\newline

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

\newline

(______,______)

\newline

(______,______)

Move and Simplify: Now, let's move everything to one side to get a quadratic equation. $\newline$ $x^2 - 27x + 14x + 9 + 31 = 0$ $\newline$ $x^2 - 13x + 40 = 0$
Factor Quadratic Equation: Next, we need to factor the quadratic equation. $\newline$ $(x - 5)(x - 8) = 0$
Solve for x: Now, we solve for x by setting each factor equal to zero. $\newline$ $x - 5 = 0$ or $x - 8 = 0$ $\newline$ So, $x = 5$ or $x = 8$
Find y-values: Let's find the corresponding y-values by plugging $x$ back into one of the original equations. $\newline$ For $x = 5$ , $y = -14(5) - 31$ which gives us $y = -70 - 31$ so $y = -101$ .
Find y-values: Now, for $x = 8$ , $y = -14(8) - 31$ which gives us $y = -112 - 31$ so $y = -143$ .
Write Coordinates: Finally, we write the coordinates in exact form. The first coordinate is $(5, -101)$ and the second coordinate is $(8, -143)$ .