The drama and math clubs have a combined membership of 72 students. One-fourth of the drama club members are eighth graders and One-eighth of the math club members are eighth graders. If there are 14 eighth graders in the two clubs, how many members does each club have? The equation x y = 72 represents the total membership of both clubs, with x representing the drama club members and y representing the math club members. What is the other equation for this scenario? x y = 14 One-fourth y one-eighth x = 14 One-fourth x 14 = one-eighth y One-fourth x one-eighth y = 14.

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