Solve the system of equations. y = -x - 24 x^2 + y^2 = 488 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

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Solve the system of equations.  y = -x - 24  x^2 + y^2 = 488          Write the coordinates in exact form. Simplify all fractions and radicals.    (______,______)  (______,______)

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Substitute and Simplify: Substitute the expression for y from the first equation into the second equation. Given the system of equations: y = -x - 24 x^2 + y^2 = 488 We substitute y in the second equation with the expression from the first equation: x^2 + (-x - 24)^2 = 488Expand and Combine Terms: Expand the squared term and simplify the equation. x^2 + (-x - 24)^2 = 488 x^2 + (x^2 + 48x + 576) = 488 Combine like terms: 2x^2 + 48x + 576 = 488Move and Simplify Further: Move all terms to one side to set the equation to zero and simplify further. 2x^2 + 48x + 576 - 488 = 0 2x^2 + 48x + 88 = 0 Divide the entire equation by 2 to simplify: x^2 + 24x + 44 = 0Factor the Quadratic: Factor the quadratic equation. We look for two numbers that multiply to 44 and add up to 24. These numbers are 22 and 2. (x + 22)(x + 2) = 0Solve for x: Solve for x by setting each factor equal to zero. x + 22 = 0 or x + 2 = 0 x = -22 or x = -2Find y-Values: Find the corresponding y-values for each x-value by substituting back into the first equation. For x = -22: y = -(-22) - 24 y = 22 - 24 y = -2  For x = -2: y = -(-2) - 24 y = 2 - 24 y = -22Write Coordinates: Write the coordinates in exact form. The solutions to the system of equations are the points where the values of x and y satisfy both equations. Therefore, the coordinates are: (-22, -2) and (-2, -22)

Solve the system of equations. $\newline$ $y = -x - 24$ $\newline$ $x^2 + y^2 = 488$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ $(\_,\_)$ $\newline$ $(\_,\_)$

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Solve the system of equations.\newliney=−x−24 y = -x - 24 y=−x−24\newlinex2+y2=488 x^2 + y^2 = 488 x2+y2=488\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(_,_) (\_,\_) (_,_)\newline(_,_) (\_,\_) (_,_)

Solve the system of equations. $\newline$ $y = -x - 24$ $\newline$ $x^2 + y^2 = 488$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ $(\_,\_)$ $\newline$ $(\_,\_)$