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Solve the system of equations.\newliney=x2+34x−11y = x^2 + 34x - 11\newliney=34x+38y = 34x + 38\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Solve a nonlinear system of equationsright chevron icon

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Q. Solve the system of equations.\newliney=x2+34x−11y = x^2 + 34x - 11\newliney=34x+38y = 34x + 38\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: Set the two equations equal to each other since they both equal yy.y=x2+34x−11y = x^2 + 34x - 11y=34x+38y = 34x + 38So, x2+34x−11=34x+38x^2 + 34x - 11 = 34x + 38.
  2. Subtract to Simplify: Subtract 34x34x from both sides to simplify the equation.\newlinex2+34x−11−34x=34x+38−34xx^2 + 34x - 11 - 34x = 34x + 38 - 34x\newlineThis simplifies to x2−11=38x^2 - 11 = 38.
  3. Add to Isolate x2x^2: Add 1111 to both sides to isolate the x2x^2 term.\newlinex2−11+11=38+11x^2 - 11 + 11 = 38 + 11\newlineThis simplifies to x2=49x^2 = 49.
  4. Take Square Root: Take the square root of both sides to solve for xx.x2=49\sqrt{x^2} = \sqrt{49}This gives us x=7x = 7 and x=−7x = -7 (since both positive and negative roots are possible).
  5. Substitute x=7x = 7: Substitute x=7x = 7 into one of the original equations to find the corresponding yy value.\newlineUsing y=34x+38y = 34x + 38, we get y=34(7)+38y = 34(7) + 38.\newlineThis simplifies to y=238+38y = 238 + 38, which equals y=276y = 276.
  6. Substitute x=−7x = -7: Substitute x=−7x = -7 into the same equation to find the corresponding yy value.\newlineUsing y=34x+38y = 34x + 38, we get y=34(−7)+38y = 34(-7) + 38.\newlineThis simplifies to y=−238+38y = -238 + 38, which equals y=−200y = -200.

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