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Solve the system of equations.\newlinex2+y2=425x^2 + y^2 = 425\newlinex=4yx = 4y\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newlinex2+y2=425x^2 + y^2 = 425\newlinex=4yx = 4y\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute x=4yx = 4y: Substitute x=4yx = 4y into x2+y2=425x^2 + y^2 = 425.
    (4y)2+y2=425(4y)^2 + y^2 = 425
    16y2+y2=42516y^2 + y^2 = 425
  2. Combine like terms: Combine like terms. 17y2=42517y^2 = 425
  3. Divide and solve for y2y^2: Divide both sides by 1717 to solve for y2y^2.y2=42517y^2 = \frac{425}{17}y2=25y^2 = 25
  4. Find yy: Take the square root of both sides to find yy.\newliney=±25y = \pm\sqrt{25}\newliney=±5y = \pm5
  5. Substitute back to find xx: Substitute yy back into x=4yx = 4y to find xx.
    x=4(5)x = 4(5) and x=4(−5)x = 4(-5)
    x=20x = 20 and x=−20x = -20
  6. Write coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (20,5)(20, 5)\newlineSecond Coordinate: (−20,−5)(-20, -5)

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