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Solve the system of equations.\newliney=−23x−26y = -23x - 26\newliney=x2−36x+4y = x^2 - 36x + 4\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=−23x−26y = -23x - 26\newliney=x2−36x+4y = x^2 - 36x + 4\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. This gives us −23x−26=x2−36x+4-23x - 26 = x^2 - 36x + 4.
  2. Rearrange and Solve: Rearrange the equation to set it to zero and solve for xx. This means we will add 23x23x to both sides and add 2626 to both sides, resulting in x2−36x+23x+4+26=0x^2 - 36x + 23x + 4 + 26 = 0, which simplifies to x2−13x+30=0x^2 - 13x + 30 = 0.
  3. Factor Quadratic Equation: Factor the quadratic equation x2−13x+30=0x^2 - 13x + 30 = 0. The factors of 3030 that add up to −13-13 are −10-10 and −3-3, so the factored form is (x−10)(x−3)=0(x - 10)(x - 3) = 0.
  4. Solve for x: Solve for x by setting each factor equal to zero. This gives us x−10=0x - 10 = 0 or x−3=0x - 3 = 0, which means x=10x = 10 or x=3x = 3.
  5. Substitute x Values: Substitute x=10x = 10 into one of the original equations to find the corresponding yy value. Using y=−23x−26y = -23x - 26, we get y=−23(10)−26y = -23(10) - 26, which simplifies to y=−230−26y = -230 - 26, resulting in y=−256y = -256.
  6. Find Corresponding y Values: Substitute x=3x = 3 into one of the original equations to find the corresponding y value. Using y=−23x−26y = -23x - 26, we get y=−23(3)−26y = -23(3) - 26, which simplifies to y=−69−26y = -69 - 26, resulting in y=−95y = -95.

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