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Solve the system of equations.\newliney=x2−37x−42y = x^2 - 37x - 42\newliney=−37x−33y = -37x - 33\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=x2−37x−42y = x^2 - 37x - 42\newliney=−37x−33y = -37x - 33\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.x2−37x−42=−37x−33x^2 - 37x - 42 = -37x - 33
  2. Cancel Out Terms: Cancel out the −37x-37x on both sides.\newlinex2−42=−33x^2 - 42 = -33
  3. Isolate x2x^2: Add 4242 to both sides to isolate x2x^2.\newlinex2=9x^2 = 9
  4. Solve for x: Take the square root of both sides to solve for x.\newlinex=3x = 3 or x=−3x = -3
  5. Substitute xx into Second Equation: Substitute xx back into the second equation to find yy.\newlineFor x=3x = 3: y=−37(3)−33=−111−33=−144y = -37(3) - 33 = -111 - 33 = -144\newlineFor x=−3x = -3: y=−37(−3)−33=111−33=78y = -37(-3) - 33 = 111 - 33 = 78
  6. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (3,−144)(3, -144)\newlineSecond Coordinate: (−3,78)(-3, 78)

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