Select the correct responses in the table. The relationship between two numbers is described below, where x represents the first number and y represents the second number.

The square of the first number is equal to the sum of the second number and 16. The difference of 4 times the second number and 1 is equal to the first number multiplied by 7.

Select the equations that form the system that models this situation. Then, select the solution(s) of the system.

Equations Solutions
y2 + 16 = x (2x)2 = y + 16 (1,15) (5,9)
x2 = y + 16 7y - 1 = 4x (2,-12) (8,48)
1 - 4y = 7x 4y - 1 = 7x (4,-7) (9,3)

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