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Solve the system of equations.\newliney=−8x+50y = -8x + 50\newliney=x2−8x−50y = x^2 - 8x - 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=−8x+50y = -8x + 50\newliney=x2−8x−50y = x^2 - 8x - 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=−8x+50y = -8x + 50\newliney=x2−8x−50y = x^2 - 8x - 50\newlineSet the two equations equal to each other to find the xx-values where their yy-values are the same.\newline−8x+50=x2−8x−50-8x + 50 = x^2 - 8x - 50
  2. Simplify Quadratic Equation: Simplify the equation by moving all terms to one side to form a quadratic equation.\newline0=x2−8x−50+8x−500 = x^2 - 8x - 50 + 8x - 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=−8x+50y = -8x + 50.\newlineFor x=10x = 10:\newliney=−8(10)+50y = -8(10) + 50\newliney=−80+50y = -80 + 50\newliney=−30y = -30
  5. Find yy for x=−10x=-10: Find the yy-value for x=−10x = -10:y=−8(−10)+50y = -8(-10) + 50y=80+50y = 80 + 50y=130y = 130
  6. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (10,−30)(10, -30)\newlineSecond Coordinate: (−10,130)(-10, 130)

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