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Solve the system of equations.\newlinex2+y2=20x^2 + y^2 = 20\newlinex=−3y+10x = -3y + 10\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=20x^2 + y^2 = 20\newlinex=−3y+10x = -3y + 10\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute xx: Substitute xx from the second equation into the first equation.\newlinex2+y2=20x^2 + y^2 = 20\newlinex=−3y+10x = -3y + 10\newline(−3y+10)2+y2=20(-3y + 10)^2 + y^2 = 20
  2. Expand and simplify: Expand the squared term and simplify.\newline(−3y+10)2=9y2−60y+100(-3y + 10)^2 = 9y^2 - 60y + 100\newline9y2−60y+100+y2=209y^2 - 60y + 100 + y^2 = 20
  3. Combine like terms: Combine like terms.\newline10y2−60y+100=2010y^2 - 60y + 100 = 20\newline10y2−60y+80=010y^2 - 60y + 80 = 0
  4. Divide and simplify: Divide the entire equation by 1010 to simplify.\newliney2−6y+8=0y^2 - 6y + 8 = 0
  5. Factor quadratic equation: Factor the quadratic equation.\newline(y−4)(y−2)=0(y - 4)(y - 2) = 0
  6. Solve for y: Solve for y by setting each factor equal to zero.\newliney−4=0y - 4 = 0 or y−2=0y - 2 = 0\newliney=4y = 4 or y=2y = 2
  7. Substitute yy into xx: Substitute yy back into x=−3y+10x = -3y + 10 to find corresponding xx values.\newlineFor y=4y = 4: x=−3(4)+10=−2x = -3(4) + 10 = -2\newlineFor y=2y = 2: x=−3(2)+10=4x = -3(2) + 10 = 4
  8. Write coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (−2,4)(-2, 4)\newlineSecond Coordinate: (4,2)(4, 2)

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