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Solve the system of equations.\newliney=x2−10x+30y = x^2 - 10x + 30\newliney=−25x−20y = -25x - 20\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=x2−10x+30y = x^2 - 10x + 30\newliney=−25x−20y = -25x - 20\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.y=x2−10x+30y = x^2 - 10x + 30y=−25x−20y = -25x - 20x2−10x+30=−25x−20x^2 - 10x + 30 = -25x - 20
  2. Form Quadratic Equation: Move all terms to one side to form a quadratic equation.\newlinex2−10x+25x+30+20=0x^2 - 10x + 25x + 30 + 20 = 0\newlinex2+15x+50=0x^2 + 15x + 50 = 0
  3. Factor Quadratic: Factor the quadratic equation.\newline(x+5)(x+10)=0(x + 5)(x + 10) = 0
  4. Solve for x: Set each factor equal to zero and solve for x.\newlinex+5=0x + 5 = 0 or x+10=0x + 10 = 0\newlinex=−5x = -5 or x=−10x = -10
  5. Substitute x=−5x = -5: Substitute x=−5x = -5 into one of the original equations to find yy.\newliney=−25(−5)−20y = -25(-5) - 20\newliney=125−20y = 125 - 20\newliney=105y = 105
  6. Substitute x=−10x = -10: Substitute x=−10x = -10 into one of the original equations to find yy.\newliney=−25(−10)−20y = -25(-10) - 20\newliney=250−20y = 250 - 20\newliney=230y = 230

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