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Solve the system of equations.\newlinex2+y2=580x^2 + y^2 = 580\newliney=−3x+30y = -3x + 30\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newlinex2+y2=580x^2 + y^2 = 580\newliney=−3x+30y = -3x + 30\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute yy into first equation: Substitute yy from the second equation into the first equation.x2+(−3x+30)2=580x^2 + (-3x + 30)^2 = 580
  2. Expand and simplify: Expand and simplify the equation. x2+9x2−180x+900=580x^2 + 9x^2 - 180x + 900 = 580
  3. Combine like terms: Combine like terms. 10x2−180x+900−580=010x^2 - 180x + 900 - 580 = 0
  4. Further simplify: Simplify the equation further. 10x2−180x+320=010x^2 - 180x + 320 = 0
  5. Divide by 1010: Divide the entire equation by 1010 to simplify. x2−18x+32=0x^2 - 18x + 32 = 0
  6. Factor the quadratic equation: Factor the quadratic equation.\newline(x−16)(x−2)=0(x - 16)(x - 2) = 0
  7. Solve for x: Solve for x by setting each factor equal to zero.\newlinex−16=0x - 16 = 0 or x−2=0x - 2 = 0
  8. Find x-values: Find the two x-values. x=16x = 16 or x=2x = 2
  9. Substitute xx into yy: Substitute xx-values into y=−3x+30y = -3x + 30 to find corresponding yy-values.\newlineFor x=16x = 16: y=−3(16)+30=−18y = -3(16) + 30 = -18\newlineFor x=2x = 2: y=−3(2)+30=24y = -3(2) + 30 = 24
  10. Write coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (16,−18)(16, -18)\newlineSecond Coordinate: (2,24)(2, 24)

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