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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineAiden is going to ship some gifts to family members, and he is considering two shipping companies. The first shipping company charges a fee of $13\$13 to ship a medium box, plus an additional $6\$6 per kilogram. A second shipping company charges $15\$15 for the same size of box, plus an additional $5\$5 per kilogram. At a certain weight, the two shipping methods will cost the same amount. How much will it cost? What is that weight?\newlineThe two shipping methods both cost $\$_____ at a weight of _____ kilograms.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineAiden is going to ship some gifts to family members, and he is considering two shipping companies. The first shipping company charges a fee of $13\$13 to ship a medium box, plus an additional $6\$6 per kilogram. A second shipping company charges $15\$15 for the same size of box, plus an additional $5\$5 per kilogram. At a certain weight, the two shipping methods will cost the same amount. How much will it cost? What is that weight?\newlineThe two shipping methods both cost $\$_____ at a weight of _____ kilograms.
  1. Define Equations: Define the equations for each company's shipping cost based on weight.\newlineLet xx be the weight in kilograms and yy be the total cost in dollars.\newlineFor the first company: y=6x+13y = 6x + 13\newlineFor the second company: y=5x+15y = 5x + 15
  2. Set Equations Equal: Set the equations equal to each other to find the weight at which the costs are the same. 6x+13=5x+156x + 13 = 5x + 15
  3. Solve for x: Solve for x by subtracting 5x5x from both sides.\newline6x−5x+13=156x - 5x + 13 = 15\newlinex+13=15x + 13 = 15
  4. Subtract to Isolate x: Subtract 1313 from both sides to isolate xx.\newlinex=15−13x = 15 - 13\newlinex=2x = 2
  5. Substitute xx: Substitute x=2x = 2 back into either original equation to find the cost. Using the first company's equation:\newliney=6(2)+13y = 6(2) + 13\newliney=12+13y = 12 + 13\newliney=25y = 25

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