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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineErnesto is going to ship some gifts to family members, and he is considering two shipping companies. The first shipping company charges a fee of $11\$11 to ship a medium box, plus an additional $2\$2 per pound. A second shipping company charges $9\$9 for the same size of box, plus an additional $3\$3 per pound. 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 _____ pounds.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineErnesto is going to ship some gifts to family members, and he is considering two shipping companies. The first shipping company charges a fee of $11\$11 to ship a medium box, plus an additional $2\$2 per pound. A second shipping company charges $9\$9 for the same size of box, plus an additional $3\$3 per pound. 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 _____ pounds.
  1. Define Variables: Let's define two variables: let xx be the weight of the package in pounds, and let yy be the total cost to ship the package. We can write two equations based on the information given for each shipping company.\newlineFor the first shipping company: y=11+2xy = 11 + 2x (since it charges $11\$11 plus $2\$2 per pound)\newlineFor the second shipping company: y=9+3xy = 9 + 3x (since it charges $9\$9 plus $3\$3 per pound)\newlineAt the weight where the two shipping methods cost the same, the yy values will be equal, so we can set the two equations equal to each other to find the weight xx.\newlineyy00
  2. Write Equations: Now we solve for xx by subtracting 2x2x from both sides of the equation to get the xx terms on one side:\newline11+2x−2x=9+3x−2x11 + 2x - 2x = 9 + 3x - 2x\newlineThis simplifies to:\newline11=9+x11 = 9 + x
  3. Solve for Weight: Next, we subtract 99 from both sides to solve for xx: \newline11−9=9+x−911 - 9 = 9 + x - 9\newlineThis simplifies to:\newline2=x2 = x\newlineSo the weight at which both shipping methods cost the same is 22 pounds.
  4. Substitute Weight: Now that we have the weight, we can substitute x=2x = 2 into either of the original equations to find the cost yy. We'll use the first company's equation:\newliney=11+2xy = 11 + 2x\newliney=11+2(2)y = 11 + 2(2)\newliney=11+4y = 11 + 4\newliney=15y = 15\newlineSo the cost at which both shipping methods cost the same is $15\$15.

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