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Solve the system of equations.\newliney=x2+8x−24y = x^2 + 8x - 24\newliney=−2x−49y = -2x - 49\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)

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Q. Solve the system of equations.\newliney=x2+8x−24y = x^2 + 8x - 24\newliney=−2x−49y = -2x - 49\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)
  1. Set Equations Equal: Set the two equations equal to each other since they both equal yy.x2+8x−24=−2x−49x^2 + 8x - 24 = -2x - 49
  2. Move Terms to One Side: Move all terms to one side to set the equation to zero.\newlinex2+8x+2x−24+49=0x^2 + 8x + 2x - 24 + 49 = 0\newlinex2+10x+25=0x^2 + 10x + 25 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation.\newline(x+5)(x+5)=0(x + 5)(x + 5) = 0
  4. Solve for x: Solve for x by setting each factor equal to zero.\newlinex+5=0x + 5 = 0\newlinex=−5x = -5
  5. Substitute xx for yy: Substitute xx back into one of the original equations to find yy. Using y=−2x−49y = -2x - 49: y=−2(−5)−49y = -2(-5) - 49 y=10−49y = 10 - 49 y=−39y = -39
  6. Write Coordinates: Write the coordinates in exact form.\newlineThe solution to the system is (−5,−39)(-5, -39).

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