Solve the system of equations. y = x^2 - 18x - 9 y = -5x + 39 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = x^2 - 18x - 9 y = -5x + 39 To find the solution, we will set the two equations equal to each other because they both equal y. x^2 - 18x - 9 = -5x + 39Rearrange and Form Quadratic Equation: Rearrange the equation to bring all terms to one side and form a standard quadratic equation. x^2 - 18x - 9 + 5x - 39 = 0 x^2 - 13x - 48 = 0Factor Quadratic Equation: Factor the quadratic equation. We need to find two numbers that multiply to -48 and add up to -13. These numbers are -16 and 3. x^2 - 16x + 3x - 48 = 0 (x - 16)(x + 3) = 0Solve for x: Solve for x by setting each factor equal to zero. (x - 16) = 0 or (x + 3) = 0 x = 16 or x = -3Find Corresponding y-Values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. We can use y = -5x + 39. For x = 16: y = -5(16) + 39 y = -80 + 39 y = -41 For x = -3: y = -5(-3) + 39 y = 15 + 39 y = 54Write Coordinates: Write the coordinates in exact form. The solutions to the system of equations are the points where the two graphs intersect, which are the x-values we found and their corresponding y-values. First Coordinate: (16, -41) Second Coordinate: (-3, 54)

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Solve the system of equations. $\newline$ $y = x^2 - 18x - 9$ $\newline$ $y = -5x + 39$ $\newline$ 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 = x^2 - 18x - 9

\newline

y = -5x + 39

\newline

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = x^2 - 18x - 9$ $\newline$ $y = -5x + 39$ $\newline$ To find the solution, we will set the two equations equal to each other because they both equal $y$ . $\newline$ $x^2 - 18x - 9 = -5x + 39$
Rearrange and Form Quadratic Equation: Rearrange the equation to bring all terms to one side and form a standard quadratic equation. $\newline$ $x^2 - 18x - 9 + 5x - 39 = 0$ $\newline$ $x^2 - 13x - 48 = 0$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $-48$ and add up to $-13$ . These numbers are $-16$ and $3$ . $\newline$ $x^2 - 16x + 3x - 48 = 0$ $\newline$ $(x - 16)(x + 3) = 0$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $(x - 16) = 0$ or $(x + 3) = 0$ $\newline$ $x = 16$ or $x = -3$
Find Corresponding y-Values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. We can use $y = -5x + 39$ . $\newline$ For $x = 16$ : $\newline$ $y = -5(16) + 39$ $\newline$ $y = -80 + 39$ $\newline$ $y = -41$ $\newline$ For $x = -3$ : $\newline$ $y = -5(-3) + 39$ $\newline$ $y = 15 + 39$ $\newline$ $y = 54$
Write Coordinates: Write the coordinates in exact form. $\newline$ The solutions to the system of equations are the points where the two graphs intersect, which are the $x$ -values we found and their corresponding $y$ -values. $\newline$ First Coordinate: $(16, -41)$ $\newline$ Second Coordinate: $(-3, 54)$