Question 1

carly and janiya put some money into their money boxes every week. the amounts of money (y), in dollars, in their money boxes after certain amounts of time (x), in weeks, are shown by the equations below:

carly
y = 60x + 40

janiya
y = 50x + 80

after how many weeks will carly and janiya have the same amount of money in their money boxes and what will that amount be?
5 weeks, $280
5 weeks, $340
4 weeks, $280
4 weeks, $340

question 2

a system of equations is shown below:

y = 8x − 2
y = 9x − 7

what is the solution to the system of equations?
(−5, 38)
(−5, −38)
(5, 38)
(5, −38)

question 3

two equations are given below:

m + 3n = 10
m = n − 2

what is the solution to the set of equations in the form (m, n)?
(1, 3)
(2, 4)
(0, 2)
(4, 6)

question 4

the work of a student to solve a set of equations is shown:

equation 1: m = 8 + 2n
equation 2: 3m = 4 + 4n

step 1:
−3(m) =
−3(8 + 2n)
[equation 1 is multiplied by −3.]

3m =
4 + 4n
[equation 2]

step 2:
−3m =
−24 − 6n
[equation 1 in step 1 is simplified.]

3m =
4 + 4n
[equation 2]

step 3:
−3m + 3m =
−24 − 6n + 4n
[equations in step 2 are added.]

step 4:
0 =
−24 − 2n

step 5:
n =
−12

in which step did the student first make an error?

step 4
step 3
step 2
step 1

question 5

a student is trying to solve the system of two equations given below:

equation p: y + z = 6
equation q: 8y + 7z = 1

which of the following is a possible step used in eliminating the y-term?
(y + z = 6) ⋅ −8
(y + z = 6) ⋅ 7
(8y + 7z = 1) ⋅ 7
(8y + 7z = 1) ⋅ 8

question 6

line a is represented by the equation given below:

x + y = 4

what is most likely the equation for line b, so that the set of equations has infinitely many solutions?
4x + 4y = 4
4x + y = 4
2x + 2y = 8
x + y = 8