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Solve the system of equations.\newlinex2+y2=325x^2 + y^2 = 325\newliney=−2x−20y = -2x - 20\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)\newline

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Q. Solve the system of equations.\newlinex2+y2=325x^2 + y^2 = 325\newliney=−2x−20y = -2x - 20\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)\newline
  1. Substitute yy into first equation: Substitute yy from the second equation into the first equation.x2+(−2x−20)2=325x^2 + (-2x - 20)^2 = 325
  2. Expand and simplify: Expand and simplify the equation.\newlinex2+(4x2+80x+400)=325x^2 + (4x^2 + 80x + 400) = 325\newline5x2+80x+400=3255x^2 + 80x + 400 = 325
  3. Set equation to zero: Subtract 325325 from both sides to set the equation to zero.\newline5x2+80x+75=05x^2 + 80x + 75 = 0
  4. Divide and simplify: Divide the entire equation by 55 to simplify.\newlinex2+16x+15=0x^2 + 16x + 15 = 0
  5. Factor the equation: Factor the quadratic equation.\newline(x+1)(x+15)=0(x + 1)(x + 15) = 0
  6. Solve for x: Solve for x by setting each factor equal to zero.\newlinex+1=0x + 1 = 0 or x+15=0x + 15 = 0\newlinex=−1x = -1 or x=−15x = -15
  7. Substitute xx into yy: Substitute xx values into y=−2x−20y = -2x - 20 to find corresponding yy values.\newlineFor x=−1x = -1: y=−2(−1)−20=2−20=−18y = -2(-1) - 20 = 2 - 20 = -18\newlineFor x=−15x = -15: y=−2(−15)−20=30−20=10y = -2(-15) - 20 = 30 - 20 = 10

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