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Solve the system of equations.\newliney=x2+44x+8y = x^2 + 44x + 8\newliney=44x+44y = 44x + 44\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+44x+8y = x^2 + 44x + 8\newliney=44x+44y = 44x + 44\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+44x+8y = x^2 + 44x + 8y=44x+44y = 44x + 44So, x2+44x+8=44x+44x^2 + 44x + 8 = 44x + 44
  2. Subtract and Simplify: Subtract 44x+4444x + 44 from both sides to set the equation to zero.\newlinex2+44x+8−(44x+44)=0x^2 + 44x + 8 - (44x + 44) = 0\newlineThis simplifies to x2−36=0x^2 - 36 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation. x2−36=(x+6)(x−6)=0x^2 - 36 = (x + 6)(x - 6) = 0
  4. Solve for x: Solve for x using the zero product property.\newlinex+6=0x + 6 = 0 or x−6=0x - 6 = 0\newlineThis gives us x=−6x = -6 or x=6x = 6
  5. Substitute x=−6x = -6: Substitute x=−6x = -6 into one of the original equations to find the corresponding yy value.\newlineUsing y=44x+44y = 44x + 44, we get y=44(−6)+44=−264+44=−220y = 44(-6) + 44 = -264 + 44 = -220\newlineSo one point of intersection is (−6,−220)(-6, -220).
  6. Substitute x=6x = 6: Substitute x=6x = 6 into one of the original equations to find the corresponding yy value.\newlineUsing y=44x+44y = 44x + 44, we get y=44(6)+44=264+44=308y = 44(6) + 44 = 264 + 44 = 308\newlineSo the other point of intersection is (6,308)(6, 308).

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