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Solve the system of equations.\newliney=2x−20y = 2x - 20\newlinex2+y2=260x^2 + y^2 = 260\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=2x−20y = 2x - 20\newlinex2+y2=260x^2 + y^2 = 260\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=2x−20y = 2x - 20\newlinex2+y2=260x^2 + y^2 = 260\newlinex2+(2x−20)2=260x^2 + (2x - 20)^2 = 260
  2. Expand and simplify: Expand and simplify the equation.\newlinex2+(2x−20)(2x−20)=260x^2 + (2x - 20)(2x - 20) = 260\newlinex2+4x2−80x+400=260x^2 + 4x^2 - 80x + 400 = 260\newline5x2−80x+140=2605x^2 - 80x + 140 = 260
  3. Subtract 260260: Subtract 260260 from both sides to set the equation to zero.\newline5x2−80x+400−260=05x^2 - 80x + 400 - 260 = 0\newline5x2−80x+140=05x^2 - 80x + 140 = 0
  4. Divide and simplify: Divide the entire equation by 55 to simplify.x2−16x+28=0x^2 - 16x + 28 = 0
  5. Factor the equation: Factor the quadratic equation.\newline(x−14)(x−2)=0(x - 14)(x - 2) = 0
  6. Solve for x: Solve for x by setting each factor equal to zero.\newlinex−14=0x - 14 = 0 or x−2=0x - 2 = 0\newlinex=14x = 14 or x=2x = 2
  7. Find corresponding y values: Find the corresponding y values for each xx.\newlineFor x=14x = 14: y=2(14)−20=28−20=8y = 2(14) - 20 = 28 - 20 = 8\newlineFor x=2x = 2: y=2(2)−20=4−20=−16y = 2(2) - 20 = 4 - 20 = -16
  8. Write coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (14,8)(14, 8)\newlineSecond Coordinate: (2,−16)(2, -16)

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