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Solve the system of equations.\newliney=17x+37y = 17x + 37\newliney=x2+33x+20y = x^2 + 33x + 20\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Q. Solve the system of equations.\newliney=17x+37y = 17x + 37\newliney=x2+33x+20y = x^2 + 33x + 20\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute yy Equation: Substitute yy from the first equation into the second equation. Since y=17x+37y = 17x + 37, we can replace yy in the second equation with 17x+3717x + 37. This gives us 17x+37=x2+33x+2017x + 37 = x^2 + 33x + 20.
  2. Rearrange and Solve: Rearrange the equation to set it to zero and solve for xx. This means we subtract 17x+3717x + 37 from both sides to get 0=x2+33x+20−17x−370 = x^2 + 33x + 20 - 17x - 37.
  3. Simplify Equation: Simplify the equation by combining like terms. This gives us 0=x2+16x−170 = x^2 + 16x - 17.
  4. Factor Quadratic Equation: Factor the quadratic equation x2+16x−17x^2 + 16x - 17. We are looking for two numbers that multiply to −17-17 and add up to 1616. These numbers are 1717 and −1-1. So we can write the equation as (x+17)(x−1)=0(x + 17)(x - 1) = 0.
  5. Solve for x: Solve for x by setting each factor equal to zero. This gives us two solutions: x+17=0x + 17 = 0 or x−1=0x - 1 = 0. Therefore, x=−17x = -17 or x=1x = 1.
  6. Substitute x=−17x = -17: Substitute x=−17x = -17 into the first equation y=17x+37y = 17x + 37 to find the corresponding value of yy. This gives us y=17(−17)+37y = 17(-17) + 37.
  7. Calculate yy for x=−17x = -17: Calculate the value of yy when x=−17x = -17. This gives us y=−289+37y = -289 + 37, which simplifies to y=−252y = -252.
  8. Substitute x=1x = 1: Substitute x=1x = 1 into the first equation y=17x+37y = 17x + 37 to find the corresponding value of yy. This gives us y=17(1)+37y = 17(1) + 37.
  9. Calculate yy for x=1x = 1: Calculate the value of yy when x=1x = 1. This gives us y=17+37y = 17 + 37, which simplifies to y=54y = 54.

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