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Solve the system of equations.\newliney=7x2+18x−14y = 7x^2 + 18x - 14\newliney=18x−7y = 18x - 7\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=7x2+18x−14y = 7x^2 + 18x - 14\newliney=18x−7y = 18x - 7\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.7x2+18x−14=18x−77x^2 + 18x - 14 = 18x - 7
  2. Subtract xx Terms: Subtract 18x18x from both sides to get the xx terms on one side.\newline7x2+18x−18x−14=18x−18x−77x^2 + 18x - 18x - 14 = 18x - 18x - 7\newline7x2−14=−77x^2 - 14 = -7
  3. Add to Isolate: Add 77 to both sides to isolate the quadratic term.\newline7x2−14+7=−7+77x^2 - 14 + 7 = -7 + 7\newline7x2−7=07x^2 - 7 = 0
  4. Factor Out: Factor out a 77 from the left side.\newline7(x2−1)=07(x^2 - 1) = 0
  5. Set Inside Equal: Set the inside of the parentheses equal to zero.\newlinex2−1=0x^2 - 1 = 0
  6. Factor Left Side: Factor the left side as a difference of squares.\newline(x+1)(x−1)=0(x + 1)(x - 1) = 0
  7. Set Factors Equal: Set each factor equal to zero and solve for xx.x+1=0x + 1 = 0 or x−1=0x - 1 = 0x=−1x = -1 or x=1x = 1
  8. Plug x=−1x = -1: Plug x=−1x = -1 into the second equation y=18x−7y = 18x - 7 to find the corresponding yy value.\newliney=18(−1)−7y = 18(-1) - 7\newliney=−18−7y = -18 - 7\newliney=−25y = -25
  9. Plug x=1x = 1: Plug x=1x = 1 into the second equation y=18x−7y = 18x - 7 to find the corresponding yy value.\newliney=18(1)−7y = 18(1) - 7\newliney=18−7y = 18 - 7\newliney=11y = 11
  10. Write Coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (−1,−25)(-1, -25)\newlineSecond Coordinate: (1,11)(1, 11)

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