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Solve the system of equations.\newliney=x2+40x−50y = x^2 + 40x - 50\newliney=40x+50y = 40x + 50\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Solve a nonlinear system of equationsright chevron icon

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Q. Solve the system of equations.\newliney=x2+40x−50y = x^2 + 40x - 50\newliney=40x+50y = 40x + 50\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+40x−50y = x^2 + 40x - 50y=40x+50y = 40x + 50So, x2+40x−50=40x+50x^2 + 40x - 50 = 40x + 50.
  2. Subtract to Zero: Subtract 40x+5040x + 50 from both sides to set the equation to zero.\newlinex2+40x−50−40x−50=0x^2 + 40x - 50 - 40x - 50 = 0\newlineThis simplifies to x2−100=0x^2 - 100 = 0.
  3. Factor Quadratic Equation: Factor the quadratic equation. x2−100=(x+10)(x−10)=0x^2 - 100 = (x + 10)(x - 10) = 0
  4. Solve for x: Solve for x by setting each factor equal to zero.\newlinex+10=0x + 10 = 0 or x−10=0x - 10 = 0\newlineThis gives us x=−10x = -10 or x=10x = 10.
  5. Substitute xx Values: Substitute x=−10x = -10 into one of the original equations to find the corresponding yy value.\newlineUsing y=40x+50y = 40x + 50, we get y=40(−10)+50=−400+50=−350y = 40(-10) + 50 = -400 + 50 = -350.
  6. Find Corresponding y: Substitute x=10x = 10 into one of the original equations to find the corresponding y value.\newlineUsing y=40x+50y = 40x + 50, we get y=40(10)+50=400+50=450y = 40(10) + 50 = 400 + 50 = 450.
  7. Write Coordinate Points: Write the solution as coordinate points.\newlineThe coordinate points are (−10,−350)(-10, -350) and (10,450)(10, 450).

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