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Solve the system of equations.\newliney=5x2+13x−10y = 5x^2 + 13x - 10\newliney=13x+10y = 13x + 10\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Solve a system of linear and quadratic equations: parabolasright chevron icon

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Q. Solve the system of equations.\newliney=5x2+13x−10y = 5x^2 + 13x - 10\newliney=13x+10y = 13x + 10\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: Set the two equations equal to each other since they both equal yy.5x2+13x−10=13x+105x^2 + 13x - 10 = 13x + 10
  2. Subtract and Set to Zero: Subtract 13x+1013x + 10 from both sides to move all terms to one side and set the equation to zero.\newline5x2+13x−10−13x−10=13x+10−13x−105x^2 + 13x - 10 - 13x - 10 = 13x + 10 - 13x - 10\newline5x2−20=05x^2 - 20 = 0
  3. Add to Isolate Quadratic Term: Add 2020 to both sides to isolate the quadratic term.\newline5x2−20+20=0+205x^2 - 20 + 20 = 0 + 20\newline5x2=205x^2 = 20
  4. Divide to Solve for x2x^2: Divide both sides by 55 to solve for x2x^2.5x25=205\frac{5x^2}{5} = \frac{20}{5}x2=4x^2 = 4
  5. Take Square Root for x: Take the square root of both sides to solve for x.\newlinex2=4\sqrt{x^2} = \sqrt{4}\newlinex=2x = 2 or x=−2x = -2
  6. Substitute x=2x = 2: Substitute x=2x = 2 into the second equation to find the corresponding yy value.\newliney=13(2)+10y = 13(2) + 10\newliney=26+10y = 26 + 10\newliney=36y = 36
  7. Substitute x=−2x = -2: Substitute x=−2x = -2 into the second equation to find the corresponding yy value.y=13(−2)+10y = 13(-2) + 10y=−26+10y = -26 + 10y=−16y = -16
  8. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (2,36)(2, 36)\newlineSecond Coordinate: (−2,−16)(-2, -16)

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