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Solve the system of equations.\newliney=20x−34y = 20x - 34\newliney=x2+12x−18y = x^2 + 12x - 18\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)

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Q. Solve the system of equations.\newliney=20x−34y = 20x - 34\newliney=x2+12x−18y = x^2 + 12x - 18\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)
  1. Set Equations Equal: We have the system of equations:\newliney=20x−34y = 20x - 34\newliney=x2+12x−18y = x^2 + 12x - 18\newlineTo find the intersection points, set the two equations equal to each other.\newline20x−34=x2+12x−1820x - 34 = x^2 + 12x - 18
  2. Rearrange and Identify Quadratic: Rearrange the equation to set it to zero and identify the quadratic equation.\newline20x−34−x2−12x+18=020x - 34 - x^2 - 12x + 18 = 0\newline−x2+8x−16=0-x^2 + 8x - 16 = 0
  3. Multiply by −1-1: Multiply the entire equation by −1-1 to make the x2x^2 term positive.\newlinex2−8x+16=0x^2 - 8x + 16 = 0
  4. Factor Quadratic Equation: Factor the quadratic equation.\newlineThe factors of 1616 that add up to 88 are 44 and 44, so the factored form is:\newline(x−4)(x−4)=0(x - 4)(x - 4) = 0
  5. Solve for x: Solve for x.\newlineSince both factors are the same, we only have one solution for xx:\newlinex−4=0x - 4 = 0\newlinex=4x = 4
  6. Find Corresponding y-Value: Find the corresponding y-value by substituting x=4x = 4 into one of the original equations.\newlineUsing y=20x−34y = 20x - 34:\newliney=20(4)−34y = 20(4) - 34\newliney=80−34y = 80 - 34\newliney=46y = 46
  7. Write Coordinates: Write the coordinates in exact form.\newlineSince we only have one solution for xx, there is only one intersection point.\newlineThe coordinates of the intersection point are (4,46)(4, 46).

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