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Solve the system of equations.\newliney=−22x−8y = -22x - 8\newliney=x2−40x+37y = x^2 - 40x + 37\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=−22x−8y = -22x - 8\newliney=x2−40x+37y = x^2 - 40x + 37\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=−22x−8y = -22x - 8\newliney=x2−40x+37y = x^2 - 40x + 37\newlineSet the two equations equal to each other to find the xx-values where their yy-values are the same.\newline−22x−8=x2−40x+37-22x - 8 = x^2 - 40x + 37
  2. Rearrange to Standard Form: Rearrange the equation to get a standard form quadratic equation.\newlinex2−40x+37+22x+8=0x^2 - 40x + 37 + 22x + 8 = 0\newlinex2−18x+45=0x^2 - 18x + 45 = 0
  3. Factor Quadratic Equation: Factor the quadratic equation.\newlineWe are looking for two numbers that multiply to 4545 and add up to −18-18. These numbers are −15-15 and −3-3.\newline(x−15)(x−3)=0(x - 15)(x - 3) = 0
  4. Solve for x: Solve for x by setting each factor equal to zero.\newlinex−15=0x - 15 = 0 or x−3=0x - 3 = 0\newlinex=15x = 15 or x=3x = 3
  5. Find Corresponding y-values: Find the corresponding y-values for each x-value by substituting back into one of the original equations. We can use y=−22x−8y = -22x - 8.\newlineFor x=15x = 15:\newliney=−22(15)−8y = -22(15) - 8\newliney=−330−8y = -330 - 8\newliney=−338y = -338\newlineFor x=3x = 3:\newliney=−22(3)−8y = -22(3) - 8\newliney=−66−8y = -66 - 8\newliney=−74y = -74

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