A.REI.5 [576929]
Student
Class
Date
1.
In order to solve the system of equations
using the elimination
method, which of the following steps could be used?
A. Multiply the first equation by 2 and then add that result to the second
equation.
B. Multiply the first equation by 3 and then add that result to the second
equation.
C. Multiply the second equation by 2 and then add that result to the first
equation.
D. Multiply the second equation by 3 and then add that result to the first
equation.
2. Arthur was solving the system of equations below:
Arthur multiplied the first equation (I) by 2 and added the product to the
second equation (II). The sum was the equation seen below:
When Arthur solved for y, he got 3. Substituting 3 into the first equation
(I), he found that x was 2.
Use Arthur's answers to show that his solution works for the second
equation (II).
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3. Which statement explains why the two systems of equations below have
the same solution?
A. The first equation in B is the sum of the equations in A, while the
other is obtained by multiplying the second equation in A by 6.
B. The first equation in B is the sum of the equations in A, while the
other is obtained by multiplying the first equation in A by 2.
C. The equations in A are increased by
B.
and
to get the equations in
D. The equations in A are multiplied by 2 and 4 to get the equations in B.
4. Which systems of equations have the same solutions?
A. L and M
B. L and N
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C. M and N
D. L, M, and N
5. Jolene is solving the system of equations shown below.
Which of these systems of equations has the same solution?
A.
B.
C.
D.
6. A student began solving a system of equations.
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The student changed the system of equations as shown.
Which mathematical property justifies this change?
A. addition property of equality
B. multiplicative identity property
C. substitution property of equality
D. multiplication property of equality
7. Which statement explains that the systems of equations shown below
have the same solution?
System A:
System B:
A. One of the equations in B is the sum of both of the original equations
in A.
B. One of the equations in B is the product of both of the original
equations in A.
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C. One of the equations in B is obtained from multiplying an equation in
A by 3 and then adding both equations in A.
D. One of the equations in B is obtained from multiplying an equation in
A by –3 and then adding both equations in A.
8. Using the elimination method, Joe solved the system of equations
for y with the following steps.
Which statement correctly identifies the mistake Joe made?
A. In step 3, Joe multiplied the term
B. In step 4, Joe simplified
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by instead of by
as instead of simplifying to
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C. In step 2, Joe should have multiplied the first equation by
by
instead of
D. In step 5, Joe should have added to both sides of the equation
instead of dividing both sides of the equation by
9. Which system of equations has the same solutions as the system below?
A.
B.
C.
D.
10. Use the system of equations for each part of the problem.
Part A. Find the equation that results from adding the first equation to
three times the second equation. Then find the equation that results from
taking the first equation minus two times the second equation.
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Part B. Show that the values of x and y obtained from solving these new
equations are also the solutions of the original system of equations.
Use words, numbers, and/or pictures to show your work.
11. A school held a charity concert over two days, collecting $2,400 the first
day and $1,400 the second day. The system of equations
and
can be used to determine x, the
cost of an adult ticket, and y, the cost of a child ticket.


Use the multiplication property of equality to rewrite the system so
that the coefficients of the variable y are the same for both equations.
Find the cost of an adult ticket and the cost of a child ticket.
12. In the following solution to a system of two equations, what property
completes the justifications?
System of Equations
Justification
Given
??
Addition Property of Equality
Division Property of Equality
Substitution
Subtraction Property of Equality
Division Property of Equality
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