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Solve the system of equations.\newliney=6x+15y = 6x + 15\newliney=x2+6x−49y = x^2 + 6x - 49\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=6x+15y = 6x + 15\newliney=x2+6x−49y = x^2 + 6x - 49\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Substitute yy into second equation: Substitute yy from the first equation into the second equation: x2+6x−49=6x+15x^2 + 6x - 49 = 6x + 15.
  2. Simplify the equation: Simplify the equation: x2+6x−6x−49−15=0x^2 + 6x - 6x - 49 - 15 = 0, which simplifies to x2−64=0x^2 - 64 = 0.
  3. Factor the equation: Factor the equation: (x+8)(x−8)=0(x + 8)(x - 8) = 0.
  4. Find values of x: Find the values of x: x+8=0x + 8 = 0 or x−8=0x - 8 = 0, so x=−8x = -8 or x=8x = 8.
  5. Substitute x=−8x = -8 for yy: Substitute x=−8x = -8 into the first equation to find yy: y=6(−8)+15y = 6(-8) + 15, which simplifies to y=−48+15y = -48 + 15, so y=−33y = -33.
  6. Substitute x=8x = 8 for yy: Substitute x=8x = 8 into the first equation to find yy: y=6(8)+15y = 6(8) + 15, which simplifies to y=48+15y = 48 + 15, so y=63y = 63.

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