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Solve the system of equations.\newliney=−3x−25y = -3x - 25\newlinex2+y2=125x^2 + y^2 = 125\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=−3x−25y = -3x - 25\newlinex2+y2=125x^2 + y^2 = 125\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute yy: Substitute yy from the first equation into the second equation.\newliney=−3x−25y = -3x - 25\newlinex2+y2=125x^2 + y^2 = 125\newlinex2+(−3x−25)2=125x^2 + (-3x - 25)^2 = 125
  2. Expand and simplify: Expand and simplify the equation.\newlinex2+(9x2+150x+625)=125x^2 + (9x^2 + 150x + 625) = 125\newline10x2+150x+625=12510x^2 + 150x + 625 = 125
  3. Subtract 125125: Subtract 125125 from both sides to set the equation to zero.\newline10x2+150x+625−125=010x^2 + 150x + 625 - 125 = 0\newline10x2+150x+500=010x^2 + 150x + 500 = 0
  4. Divide and simplify: Divide the entire equation by 1010 to simplify.\newlinex2+15x+50=0x^2 + 15x + 50 = 0
  5. Factor the equation: Factor the quadratic equation.\newline(x+10)(x+5)=0(x + 10)(x + 5) = 0
  6. Solve for x: Solve for x by setting each factor equal to zero.\newlinex+10=0x + 10 = 0 or x+5=0x + 5 = 0\newlinex=−10x = -10 or x=−5x = -5
  7. Find y-values: Find the corresponding y-values for each x-value.\newlineFor x=−10x = -10: y=−3(−10)−25=30−25=5y = -3(-10) - 25 = 30 - 25 = 5\newlineFor x=−5x = -5: y=−3(−5)−25=15−25=−10y = -3(-5) - 25 = 15 - 25 = -10
  8. Write coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (−10,5)(-10, 5)\newlineSecond Coordinate: (−5,−10)(-5, -10)

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