Solve the system of equations. y = -48x + 10 y = x^2 - 48x - 39 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

Set Equations Equal: We have the system of equations: y = -48x + 10 y = x^2 - 48x - 39 Set the two equations equal to each other to find the x-values where they intersect. -48x + 10 = x^2 - 48x - 39Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. 0 = x^2 - 48x + 48x - 39 - 10 0 = x^2 - 49Factor Quadratic Equation: Factor the quadratic equation. 0 = (x - 7)(x + 7)Solve for x: Solve for x by setting each factor equal to zero. (x - 7) = 0 or (x + 7) = 0 x = 7 or x = -7Substitute x into Equation: Find the corresponding y-values for each x-value by substituting back into one of the original equations. Let's use y = -48x + 10. For x = 7: y = -48(7) + 10 y = -336 + 10 y = -326Find y for x = -7: Find the y-value for x = -7: y = -48(-7) + 10 y = 336 + 10 y = 346Write Coordinates: Write the coordinates in exact form. First Coordinate: (7, -326) Second Coordinate: (-7, 346)

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Solve the system of equations. $\newline$ $y = -48x + 10$ $\newline$ $y = x^2 - 48x - 39$ $\newline$ $\newline$ 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.

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y = -48x + 10

\newline

y = x^2 - 48x - 39

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

\newline

(______,______)

\newline

(______,______)

Set Equations Equal: We have the system of equations: $\newline$ $y = -48x + 10$ $\newline$ $y = x^2 - 48x - 39$ $\newline$ Set the two equations equal to each other to find the $x$ -values where they intersect. $\newline$ $-48x + 10 = x^2 - 48x - 39$
Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. $\newline$ $0 = x^2 - 48x + 48x - 39 - 10$ $\newline$ $0 = x^2 - 49$
Factor Quadratic Equation: Factor the quadratic equation. $\newline$ $0 = (x - 7)(x + 7)$
Solve for x: Solve for x by setting each factor equal to zero. $\newline$ $(x - 7) = 0$ or $(x + 7) = 0$ $\newline$ $x = 7$ or $x = -7$
Substitute $x$ into Equation: Find the corresponding $y$ -values for each $x$ -value by substituting back into one of the original equations. Let's use $y = -48x + 10$ . For $x = 7$ : $y = -48(7) + 10$ $y = -336 + 10$ $y = -326$
Find $y$ for $x = -7$ : Find the $y$ -value for $x = -7$ :
$y = -48(-7) + 10$
$y = 336 + 10$
$y = 346$
Write Coordinates: Write the coordinates in exact form. $\newline$ First Coordinate: $(7, -326)$ $\newline$ Second Coordinate: $(-7, 346)$