Premier bank is planning to have a new building constructed. they would like the length of the building to be 40 feet longer than its width. to fit their needs, each floor of the building will add 12 feet to the height of the building. the cost of the foundation of the building will be $10 per square foot. the cost for each successive floor of the building will be $35,000. they plan to spend $1,180,000 on construction. they would also like the perimeter of the building to be 3 times the height of the building. create a system of equations to model the situation above, and use it to determine how many of the solutions are viable. note: the bank wants the building to be as close to their specifications as possible, but the solution does not need to include whole numbers in order to be considered viable.

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24