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Solve the system of equations.\newliney=−3x+3y = -3x + 3\newliney=x2+10x+33y = x^2 + 10x + 33\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=−3x+3y = -3x + 3\newliney=x2+10x+33y = x^2 + 10x + 33\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 to find xx. This gives us −3x+3=x2+10x+33-3x + 3 = x^2 + 10x + 33.
  2. Rearrange and solve for x: Rearrange the equation to set it to zero and solve for x. This gives us x2+10x+33+3x−3=0x^2 + 10x + 33 + 3x - 3 = 0, which simplifies to x2+13x+30=0x^2 + 13x + 30 = 0.
  3. Factor the quadratic equation: Factor the quadratic equation. The factors of 3030 that add up to 1313 are 33 and 1010, so the factored form is (x+3)(x+10)=0(x + 3)(x + 10) = 0.
  4. Solve for x: Set each factor equal to zero and solve for x. This gives us x+3=0x + 3 = 0 or x+10=0x + 10 = 0, which means x=−3x = -3 or x=−10x = -10.
  5. Substitute x=−3x = -3: Substitute x=−3x = -3 into the first equation to find the corresponding yy value. This gives us y=−3(−3)+3y = -3(-3) + 3, which simplifies to y=9+3y = 9 + 3 and then y=12y = 12.
  6. Substitute x=−10x = -10: Substitute x=−10x = -10 into the first equation to find the corresponding yy value. This gives us y=−3(−10)+3y = -3(-10) + 3, which simplifies to y=30+3y = 30 + 3 and then y=33y = 33.

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