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
Report
by EvilEvie 10.05.2018
Answers
SamanthaBees · Beginner
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MsEHolt Brainly Teacher
#1) 4 weeks, $280
#2) (5, 38)
#3) (1, 3)
#4) Step 3
#5) (y+z=6)*-8
#6) 2x+2y=8
Explanation
#1) Setting them equal,
60x+40=50x+80
Subtract 50x from both sides:
60x+40-50x=50x+80-50x
10x+40=80
Subtract 40 from both sides:
10x+40-40=80-40
10x=40
Divide both sides by 10:
10x/10 = 40/10
x=4
Plugging this in to one of our equations,
60(4)+40=240+40=280
#2) Setting the equations equal to one another,
8x-2=9x-7
Subtract 8x from both sides:
8x-2-8x=9x-7-8x
-2=x-7
Add 7 to both sides:
-2+7=x-7+7
5=x
Plugging this in to the first equation,
8(5)-2=y
40-2=y
38=y
#3) Substituting our value from the second equation into the first one,
n-2+3n=10
Combining like terms,
4n-2=10
Add 2 to both sides:
4n-2+2=10+2
4n=12
Divide both sides by 4:
4n/4 = 12/4
n=3
Substitute this into the second equation:
m=3-2=1
#4) The mistake was made on Step 3; the 4 was left off when the equations were added.
#5) To eliminate y, we want the coefficients to be the same. To accomplish this, we will multiply the first equation by -8.
#6) In order to have infinitely many solutions, we want each coefficient as well as the constant to be a multiple of our equation. Multiplying the equation by 2, we get 2x+2y=8.
