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Solve the system of equations.\newlinex2+y2=34x^2 + y^2 = 34\newlinex=4y−17x = 4y - 17\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=34x^2 + y^2 = 34\newlinex=4y−17x = 4y - 17\newline\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute xx: Substitute xx from the second equation into the first equation.\newlinex=4y−17x = 4y - 17\newlinex2+y2=34x^2 + y^2 = 34\newline(4y−17)2+y2=34(4y - 17)^2 + y^2 = 34
  2. Expand and simplify: Expand the squared term and simplify the equation.\newline(4y−17)2+y2=34(4y - 17)^2 + y^2 = 34\newline16y2−136y+289+y2=3416y^2 - 136y + 289 + y^2 = 34\newline17y2−136y+289−34=017y^2 - 136y + 289 - 34 = 0\newline17y2−136y+255=017y^2 - 136y + 255 = 0
  3. Factor quadratic equation: Factor the quadratic equation.\newline17y2−136y+255=017y^2 - 136y + 255 = 0\newline(17y−15)(y−17)=0(17y - 15)(y - 17) = 0
  4. Solve for y: Solve for y by setting each factor equal to zero.\newline17y−15=017y - 15 = 0 or y−17=0y - 17 = 0\newliney=1517y = \frac{15}{17} or y=17y = 17
  5. Substitute yy into xx: Substitute yy back into x=4y−17x = 4y - 17 to find the corresponding xx values.\newlineFor y=1517y = \frac{15}{17}:\newlinex=4(1517)−17x = 4\left(\frac{15}{17}\right) - 17\newlinex=6017−17x = \frac{60}{17} - 17\newlinex=6017−28917x = \frac{60}{17} - \frac{289}{17}\newlinex=−22917x = -\frac{229}{17}
  6. Find xx values: For y=17y = 17:x=4(17)−17x = 4(17) - 17x=68−17x = 68 - 17x=51x = 51
  7. Write coordinates: Write the coordinates in exact form.\newlineFirst Coordinate: (−22917,1517)(-\frac{229}{17}, \frac{15}{17})\newlineSecond Coordinate: (51,17)(51, 17)

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