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Solve the system of equations.\newliney=−22x+50y = -22x + 50\newliney=x2−22x−50y = x^2 - 22x - 50\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=−22x+50y = -22x + 50\newliney=x2−22x−50y = x^2 - 22x - 50\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: We have the system of equations:\newliney=−22x+50y = -22x + 50\newliney=x2−22x−50y = x^2 - 22x - 50\newlineSet the two equations equal to each other to find the xx-values where they intersect.\newline−22x+50=x2−22x−50-22x + 50 = x^2 - 22x - 50
  2. Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation.\newline0=x2−22x−50+22x−500 = x^2 - 22x - 50 + 22x - 50\newline0=x2−1000 = x^2 - 100
  3. Solve for x: Solve the quadratic equation for x.\newlinex2=100x^2 = 100\newlineTake the square root of both sides.\newlinex=±100x = \pm\sqrt{100}\newlinex=±10x = \pm10
  4. Find y-values: Find the corresponding y-values for each xx-value by substituting back into one of the original equations. Let's use y=−22x+50y = -22x + 50.\newlineFor x=10x = 10:\newliney=−22(10)+50y = -22(10) + 50\newliney=−220+50y = -220 + 50\newliney=−170y = -170
  5. Find Second y-value: Find the y-value for the second x-value.\newlineFor x=−10x = -10:\newliney=−22(−10)+50y = -22(-10) + 50\newliney=220+50y = 220 + 50\newliney=270y = 270
  6. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (10,−170)(10, -170)\newlineSecond Coordinate: (−10,270)(-10, 270)

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