Choose the word from the list that best matches each sentence.
equation identity solution variable
1. A placeholder for an unknown number.
2. A value of the variable that makes the equation true.
3. A mathematical sentence that states two quantities are equal.
4. A mathematical sentence that is true for every value.
5. In the equation x + 12 = 34, x is a.

Ivan and jeff buy a package of 8 pens for $4.00. ivan wants 5 of the pens, and jeff wants 3.how much should each student pay?

Explain how you can use the associative property to evaluate (7x50)x4.

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