Astudent has a 2% salt water solution and a 7% salt water solution. to best imitate salt water at a local beach, he needs 1 liter of a 3.5% salt water solution. he defines x as the amount of 2% solution and writes this equation:
0.2x + 0.7(x – 1) = 0.35(1)
he solves the equation and determines that x is about 1.17 liters. he interprets this as needing 1.17 liters of 2% solution to make 1 liter of 3.5% solution.

what errors did the student make? check all that apply.

→the percent values were written incorrectly in the equation.
→the amount of 7% solution should be written as 1 – x, not x – 1.
→the equation as written is solved incorrectly. x ≠ 1.17.
→x must represent the amount of the more highly concentrated solution.
→the interpretation is incorrect. 1 liter of 2% solution is needed to make 1.17 liters of 3.5% solution.

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