1. Which of the following represents a system of linear equations?
I b = c + 24
b = 2c 2 + 3c
II 15b + 4d
6.7d − c
III b = 7c − 24
c = b − 6
IV b = − 6c
c = 9
V 8b + 7cd = 57
b = 5.4c − d
VI b = 0.63c
b = c
Select all that apply.
2. Explain why 4y − 5z = 3.2 is not a system of linear equations.
3. Is (2, 1) a solution of the following system of linear equations?
table with 2 rows and 2 columns , row1 column 1 , negative 2 x plus y , column 2 equals negative 3 , row2 column 1 , x plus y , column 2 equals 3 , end table
4. Which of the ordered pairs, (6,4), (6,3), or (1,3), is a solution of the system of equations? Select all that apply.
table with 2 rows and 2 columns , row1 column 1 , negative 3 x plus 5 y , column 2 equals 12 , row2 column 1 , 7 x plus 4 y , column 2 equals 19 , end table
D. None of the ordered pairs are solutions of the system.
5. Writing You open two bank accounts. In one bank account, your initial deposit is $560 and you deposit $105 each month. Your initial deposit in the other bank account is $1,160 and you deposit $55 each month. Let d represent the total number of dollars in an account. Let t represent the time in months.
a. Which of the following systems can you use to compare how much is in each account?
A. d = 560 + 55t
d = 1,160 + 105t
B. d = 560t + 1,160
d = 105t + 55
C. d = 560 + 105t
d = 1,160 + 55t
D. d = 560t + 105
d = 1,160t + 55
b. How can using a system of equations be helpful in this situation?
a. Reasoning Is the following a system of linear equations?
z = 4x + 4y
4x = 8y + 8z
A. No, because there are more than two variables.
B. No, because only one of the equations is linear.
C. No, because there is only one equation.
D. No, because they are expressions.
E. Yes, it is a system of linear equations.
b. Does a system of linear equations always have two variables? Do you have to use the same variables in all of the equations? Explain.
7. Error Analysis A company has two branches that are growing rapidly. Branch 1 opened with 16 clients and they get 4 new clients each week. Branch 2 opened with 42 clients and they get 11 new clients each week. A manager of the company wants to compare the number of clients each branch has, n, with respect to the number of weeks since the company opened, w. The manager incorrectly uses the system of equations below to compare the number of clients for each branch.
n = 16w + 4
n = 42w + 11
a. Write a system that the manager can use to compare the number of clients for each branch.
b. What error might the manager have made?