Download A variable needs to be eliminated to solve the system of equations

CPM Algebra I
2/2010
Chapter 6 Team Test
Period_____ Name(s)
________________________
_______________________________________
CPM-Algebra
English Sentences and Mathematical Sentences
1. Match each mathematical sentence on the left with its translation on the right.
Then, for each mathematical sentence, declare what the variable “x” represents.
___a.
2x  8  22
x means_____________________
___b.
x  2(x  2)  (x  2)  22
1. Rob’s number is equal to twice Bob’s number. Cob’s number is
eight times larger than two less than Bob’s number. The sum of
Rob’s number and Cob’s number is 22.
2. Jenna earned $22 by working 2 hours and receiving an $8 bonus.
x means_____________________
___c.
2x  8(x  2)  22
3. Toby’s cup can hold 8 times as many ounces of water as Terry’s.
Together, the cups hold 22 ounces of water.
x means_____________________
___d.
x  8x  22
x means_____________________
4. A 22-ounce metal bracelet is created by mixing gold, silver, and
zinc. There are two ounces less zinc than gold, and there is twice as
much silver as zinc.
Graphs of Systems of Equations
2. Use the graph at the right for each part.
a. Write the rule/equation for each of the lines shown.
___________________ and ___________________
b. Solve the system algebraically.
c. How does the graph help you know that your solution is correct? __________________________
__________________________________________________________________________
CPM Algebra I
2/2010
Guess & Check Format to help write Equations
3. You’ve decided to give your best friend a bag of marbles for his 15th birthday. Since you know that
your friend likes red marbles better than brown ones, the number of red marbles in the bag is 4
fewer than 5 times the number of brown marbles. The bag contains 74 marbles.
a. Solve using a Guess & Check table.
Solution: _______________________________________
b. Use your Guess & Check table to help write an equation or system of equations to find out how many
of each type of marble is in the bag.
Variable(s) used: _______________________________________________
Equation(s): ___________________________________________________
c. Solve your equation/system of equations algebraically to answer the question
Solution: _______________________________________
Methods for solving systems: Graph -- Equal Values -- Substitution -- Elimination
Solve each system of equations for both variables. State your method and Show All Your Work!!
4.
5.
6.
a+b=8
3a – 4b = 3
Chosen method: _____________________
x – 2y = 6
y = 11 – 3x
Chosen method: _____________________
x = 2y + 4
x = 6y - 8
Chosen method: _____________________
Solution: ___________________________
Solution: ___________________________
Solution: ___________________________
CPM Algebra I
2/2010
Multiple Choice:
_____7.
Pearl’s work for solving this system of equations is shown here. All her work is correct.
Which method is she using?
System:
y = –5 – x
Pearl’s Solution:
2x + (–5 – x) = 20
2x + y = 20
x – 5 = 20
+5 +5
x = 25
A. Equal Values method
y = -5 –(25)
B. Substitution
y = -30
C. Elimination
D. Multiplication and then Elimination
_____8.
Edith is using substitution to solve the system of equations below.
What should the first step be?
y  3x
2x  8y  2
A. 2x  8(3x)  2
B. 3(2x  8y)  2
C. 2(3x)  8y  2
D. 3(2x  8x)  2
_____9.
Mrs. Goolsby wants to use Elimination to solve the system of equations below.
Choose the best first step.
3x  y  5
2x  3y  10
A. Multiply the first equation by 2.
B. Multiply the second equation by 3.
C. Multiply the first equation by 3.
D. Multiply the second equation by 2.
CPM Algebra I
2/2010
10. Solve the following using substitution:
X+2y=12
Y=2x+1
10____________________
11. Solve using elimination:
3x+6y=6
4x-6y=8
11.____________________
12. Sovle using any method you choose:
X+2y=9
3x+2y=7
12.____________________
13. Mr. Glass solved a system of equations using substitution and got the following result:
12= -4
a. What should he write as his final answer?
b. What does this tell you about the graph of the sytem?