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Solve the system of equations.\newliney=−9x+17y = -9x + 17\newliney=x2−6x+7y = x^2 - 6x + 7\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

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Solve a system of linear and quadratic equations: parabolasright chevron icon

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Q. Solve the system of equations.\newliney=−9x+17y = -9x + 17\newliney=x2−6x+7y = x^2 - 6x + 7\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
  1. Set Equations Equal: We have the following system of equations:\newliney=−9x+17y = -9x + 17\newliney=x2−6x+7y = x^2 - 6x + 7\newlineTo find the solution, we need to set the two equations equal to each other because they both equal yy.\newline−9x+17=x2−6x+7-9x + 17 = x^2 - 6x + 7
  2. Rearrange Equation: Rearrange the equation to get a standard form of a quadratic equation by moving all terms to one side.\newline0=x2−6x+9x+7−170 = x^2 - 6x + 9x + 7 - 17\newline0=x2+3x−100 = x^2 + 3x - 10
  3. Factor Quadratic: Factor the quadratic equation.\newlineWe are looking for two numbers that multiply to −10-10 and add up to 33. These numbers are 55 and −2-2.\newline0=(x+5)(x−2)0 = (x + 5)(x - 2)
  4. Solve for x: Solve for x by setting each factor equal to zero.\newline(x+5)=0(x + 5) = 0 or (x−2)=0(x - 2) = 0\newlinex=−5x = -5 or x=2x = 2
  5. Find yy for x=−5x=-5: Find the corresponding yy-values for each xx-value by substituting back into one of the original equations. We can use y=−9x+17y = -9x + 17.\newlineFor x=−5x = -5:\newliney=−9(−5)+17y = -9(-5) + 17\newliney=45+17y = 45 + 17\newliney=62y = 62
  6. Find yy for x=2x=2: Find the yy-value for x=2x = 2:
    y=−9(2)+17y = -9(2) + 17
    y=−18+17y = -18 + 17
    y=−1y = -1
  7. Write Coordinates: Write the coordinates in exact form.\newlineThe solutions to the system of equations are the points where the two graphs intersect, which are the xx-values we found and their corresponding yy-values.\newlineFirst Coordinate: (−5,62)(-5, 62)\newlineSecond Coordinate: (2,−1)(2, -1)

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