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Solve the system of equations.\newlinex=3y+20x = 3y + 20\newlinex2+y2=290x^2 + y^2 = 290\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newlinex=3y+20x = 3y + 20\newlinex2+y2=290x^2 + y^2 = 290\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute xx: Substitute xx from the first equation into the second equation.\newlinex=3y+20x = 3y + 20\newlinex2+y2=290x^2 + y^2 = 290\newline(3y+20)2+y2=290(3y + 20)^2 + y^2 = 290
  2. Expand and simplify: Expand the squared term and simplify the equation.\newline(3y+20)2+y2=290(3y + 20)^2 + y^2 = 290\newline9y2+120y+400+y2=2909y^2 + 120y + 400 + y^2 = 290\newline10y2+120y+400=29010y^2 + 120y + 400 = 290
  3. Subtract to set zero: Subtract 290290 from both sides to set the equation to zero.\newline10y2+120y+400−290=010y^2 + 120y + 400 - 290 = 0\newline10y2+120y+110=010y^2 + 120y + 110 = 0
  4. Divide and simplify: Divide the entire equation by 1010 to simplify.\newliney2+12y+11=0y^2 + 12y + 11 = 0
  5. Factor quadratic equation: Factor the quadratic equation.\newline(y+11)(y+1)=0(y + 11)(y + 1) = 0
  6. Solve for y: Solve for y by setting each factor equal to zero.\newliney+11=0y + 11 = 0 or y+1=0y + 1 = 0\newliney=−11y = -11 or y=−1y = -1
  7. Substitute for x(−11)x (-11): Substitute yy back into the first equation to find xx. For y=−11y = -11: x=3(−11)+20x = 3(-11) + 20 x=−33+20x = -33 + 20 x=−13x = -13
  8. Substitute for x(−1)x (-1): Substitute yy back into the first equation to find xx for the second value of yy. For y=−1y = -1: x=3(−1)+20x = 3(-1) + 20 x=−3+20x = -3 + 20 x=17x = 17
  9. Write coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (−13,−11)(-13, -11)\newlineSecond Coordinate: (17,−1)(17, -1)

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