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Solve the system of equations.\newliney=2x2−42x+4y = 2x^2 - 42x + 4\newliney=−42x+36y = -42x + 36\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=2x2−42x+4y = 2x^2 - 42x + 4\newliney=−42x+36y = -42x + 36\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.y=2x2−42x+4y = 2x^2 - 42x + 4y=−42x+36y = -42x + 362x2−42x+4=−42x+362x^2 - 42x + 4 = -42x + 36
  2. Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation. \newline2x2−42x+4+42x−36=02x^2 - 42x + 4 + 42x - 36 = 0\newline2x2−32=02x^2 - 32 = 0
  3. Solve for x: Solve the quadratic equation for x.\newline2x2=322x^2 = 32\newlinex2=16x^2 = 16\newlinex=±4x = \pm4
  4. Substitute for y: Find the corresponding yy-values for each xx-value by substituting back into one of the original equations. We'll use y=−42x+36y = -42x + 36.\newlineFor x=4x = 4:\newliney=−42(4)+36y = -42(4) + 36\newliney=−168+36y = -168 + 36\newliney=−132y = -132
  5. Find Second y-Value: Find the corresponding y-value for the second x-value.\newlineFor x=−4x = -4:\newliney=−42(−4)+36y = -42(-4) + 36\newliney=168+36y = 168 + 36\newliney=204y = 204
  6. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (4,−132)(4, -132)\newlineSecond Coordinate: (−4,204)(-4, 204)

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