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Solve the system of equations.\newliney=3xy = 3x\newlinex2+y2=160x^2 + y^2 = 160\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=3xy = 3x\newlinex2+y2=160x^2 + y^2 = 160\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute y=3xy = 3x: Substitute y=3xy = 3x into x2+y2=160x^2 + y^2 = 160.\newlinex2+(3x)2=160x^2 + (3x)^2 = 160\newlinex2+9x2=160x^2 + 9x^2 = 160\newline10x2=16010x^2 = 160
  2. Divide by 1010: Divide both sides by 1010 to solve for x2x^2.\newlinex2=16010x^2 = \frac{160}{10}\newlinex2=16x^2 = 16
  3. Take square root: Take the square root of both sides to find xx.\newlinex=±16x = \pm\sqrt{16}\newlinex=±4x = \pm4
  4. Substitute xx back: Substitute xx back into y=3xy = 3x to find yy.\newlineFor x=4x = 4: y=3(4)=12y = 3(4) = 12\newlineFor x=−4x = -4: y=3(−4)=−12y = 3(-4) = -12
  5. Write coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (4,12)(4, 12)\newlineSecond Coordinate: (−4,−12)(-4, -12)

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