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Solve the system of equations.\newliney=−17x+16y = -17x + 16\newliney=x2−18x−26y = x^2 - 18x - 26\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=−17x+16y = -17x + 16\newliney=x2−18x−26y = x^2 - 18x - 26\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: First, let's set the two equations equal to each other since they both equal yy.−17x+16=x2−18x−26-17x + 16 = x^2 - 18x - 26
  2. Move to One Side: Now, let's move everything to one side to set the equation to zero.\newlinex2−18x+17x−26−16=0x^2 - 18x + 17x - 26 - 16 = 0\newlinex2−x−42=0x^2 - x - 42 = 0
  3. Factor Quadratic Equation: Next, we need to factor the quadratic equation. Looking for two numbers that multiply to −42-42 and add up to −1-1, we get −7-7 and 66. So, (x−7)(x+6)=0(x - 7)(x + 6) = 0
  4. Solve for x: Now, solve for xx by setting each factor equal to zero.x−7=0x - 7 = 0 or x+6=0x + 6 = 0 So, x=7x = 7 or x=−6x = -6
  5. Find Corresponding y Values: We have two values for xx, let's find the corresponding yy values.\newlineSubstitute x=7x = 7 into y=−17x+16y = -17x + 16 to get y=−17(7)+16=−119+16=−103y = -17(7) + 16 = -119 + 16 = -103.\newlineSubstitute x=−6x = -6 into y=−17x+16y = -17x + 16 to get y=−17(−6)+16=102+16=118y = -17(-6) + 16 = 102 + 16 = 118.
  6. Write Coordinates: Finally, we write the coordinates in exact form.\newlineThe first coordinate is (7,−103)(7, -103).\newlineThe second coordinate is (−6,118)(-6, 118).

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