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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineOne Friday night, two large groups of people called Sparrowtown Taxi Service. The first group requested 11 sedan and 11 minivan, which can seat a total of 1010 people. The second group asked for 33 sedans and 11 minivan, which can seat a total of 1818 people. How many passengers can each type of taxi seat?\newlineA sedan can seat _____ people, and a minivan can seat _____ people.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineOne Friday night, two large groups of people called Sparrowtown Taxi Service. The first group requested 11 sedan and 11 minivan, which can seat a total of 1010 people. The second group asked for 33 sedans and 11 minivan, which can seat a total of 1818 people. How many passengers can each type of taxi seat?\newlineA sedan can seat _____ people, and a minivan can seat _____ people.
  1. Define Variables: Let's denote the number of people a sedan can seat as ss and the number of people a minivan can seat as mm. The first group's request for 11 sedan and 11 minivan seating a total of 1010 people gives us the equation s+m=10s + m = 10.
  2. Form Equations: The second group's request for 33 sedans and 11 minivan seating a total of 1818 people gives us the equation 3s+m=183s + m = 18.
  3. Eliminate Variable: We now have a system of two equations. To use elimination, we need to eliminate one of the variables, ss or mm. We choose to eliminate mm because it has the same coefficient in both equations.
  4. Subtract Equations: We subtract the first equation from the second equation to eliminate mm. This gives us 3s+m−(s+m)=18−103s + m - (s + m) = 18 - 10, which simplifies to 2s=82s = 8.
  5. Find Sedan Capacity: Dividing both sides of 2s=82s = 8 by 22, we find that s=4s = 4. This means a sedan can seat 44 people.
  6. Find Minivan Capacity: We substitute s=4s = 4 into the first equation s+m=10s + m = 10 and solve for mm. This gives us 4+m=104 + m = 10, which simplifies to m=6m = 6. This means a minivan can seat 66 people.

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