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Solve the system of equations.\newliney=−2x+10y = -2x + 10\newlinex2+y2=65x^2 + y^2 = 65\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=−2x+10y = -2x + 10\newlinex2+y2=65x^2 + y^2 = 65\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute and Simplify: Substitute yy from the first equation into the second equation.\newliney=−2x+10y = -2x + 10\newlinex2+y2=65x^2 + y^2 = 65\newlinex2+(−2x+10)2=65x^2 + (-2x + 10)^2 = 65
  2. Expand and Subtract: Expand and simplify the equation.\newlinex2+(−2x+10)2=65x^2 + (-2x + 10)^2 = 65\newlinex2+(4x2−40x+100)=65x^2 + (4x^2 - 40x + 100) = 65\newline5x2−40x+100=655x^2 - 40x + 100 = 65
  3. Divide and Simplify: Subtract 6565 from both sides to set the equation to zero.\newline5x2−40x+100−65=05x^2 - 40x + 100 - 65 = 0\newline5x2−40x+35=05x^2 - 40x + 35 = 0
  4. Factor the Equation: Divide the entire equation by 55 to simplify.\newline5x2−40x+355=05\frac{5x^2 - 40x + 35}{5} = \frac{0}{5}\newlinex2−8x+7=0x^2 - 8x + 7 = 0
  5. Solve for xx: Factor the quadratic equation.(x−7)(x−1)=0(x - 7)(x - 1) = 0
  6. Find y Values: Solve for xx by setting each factor equal to zero.\newlinex−7=0x - 7 = 0 or x−1=0x - 1 = 0\newlinex=7x = 7 or x=1x = 1
  7. Write Coordinates: Find the corresponding yy values using the first equation y=−2x+10y = -2x + 10. For x=7x = 7: y=−2(7)+10=−14+10=−4y = -2(7) + 10 = -14 + 10 = -4 For x=1x = 1: y=−2(1)+10=−2+10=8y = -2(1) + 10 = -2 + 10 = 8
  8. Write Coordinates: Find the corresponding yy values using the first equation y=−2x+10y = -2x + 10. For x=7x = 7: y=−2(7)+10=−14+10=−4y = -2(7) + 10 = -14 + 10 = -4 For x=1x = 1: y=−2(1)+10=−2+10=8y = -2(1) + 10 = -2 + 10 = 8 Write the coordinates in exact form. First Coordinate: (7,−4)(7, -4) Second Coordinate: (1,8)(1, 8)

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