Algebra 1: Systems Unit
Review
I. A-REI.5 Learning Target: I can prove that a linear
combination (i.e. elimination) is valid.
Name ______Answer Key_________
Date ____________________ Period _____
5. Solve by elimination.
3 x  4 y  18
2 x  y  3
1. Rachel wants to eliminate the x-variable to solve the
system shown. What does she need to do before
combining the equations? You do not have to solve.
x  4 y  8
2x  6 y  4
Explain:__Multiply x  4 y  8 equation by -2 so that
the x terms are opposite and will cancel out.____________
2. Rachel wants to eliminate the x-variable to solve the
system shown. What does she need to do before
combining the equations? You do not have to solve.
Answer: ____  6,9  ____
8 x  9 y  1
7 x  4 y  7
Explain:___ Multiply 8 x  9 y  1 equation by 7and the
7 x  4 y  7 equation by 8 so that the x terms will be
the same number 56 but opposite sign to cancel out._____
6. The Rodriguez family and the Wong family went
to a brunch buffet. The restaurant charges one
price for adults and another price for children.
The Rodriguez family has two adults and four
children and their bill was $52. The Wong family
has three adults and one child, and their bill was
$38. Write a system of equations to represent the
situation.
3. Is (3, 2) a solution of the system? Prove your
System: ___ 2a  4c  52 ____
answer.
____ 3a  c  38 ___
2 g  3h  0
3 g  2h  5
7. How much does the restaurant from problem #7
charge for children? For adults?
Answer: _Solution____
4. Is (-3, -5) a solution of the system? Prove your
answer.
2 x  y  1
3 x  y  12
Answer: _The restaurant charges $8 for children
Answer: _Not a Solution__
Algebra 1: Systems Unit Review Answer Key
and $10 for adults. __________________________
6/2/14
PUHSD Algebra Curriculum Team
II. A-REI.6 Learning Target: Explain why the xcoordinate of the points where the graphs of the
equations y=f(x) and y =g(x) intersect are solutions of
the equations f(x) = g(x); find the solutions
approximately.
9. Bethany and Calista are sisters who are racing
against each other. Bethany starts at the starting
line, while Calista starts a 1 mile ahead of the
starting line. Calista runs 4 miles per hour, while
Bethany runs 5 miles per hour.
Part A: Write an equation for each sister.
8. The graph of a system of linear equations is shown
below. Name the solution and explain how you know
it’s a solution.
Bethany:__ y  5 x _________
Calista:___ y  4 x  1 _________
Part B:
Draw a graph plotting the progress of both runners in
a 3-hour race.
Solution: ___No Solution_______
Explain:__The lines never intersect therefore there no
solution that would make both equations true._____
8. Part A: Identify the point of intersection.
y  x 1
3
y   x4
2
Part C: Who would win a ½ -hour race? A 1-hour
race? A 6-hour race?
Point of intersection: __  2,  1 _____
½ -Hour: __Calista___
Part B: Justify the x-coordinate from the point of
3
intersection is a solution of x  1   x  4 .
2
3
x 1   x  4
2
3
 2   1    2   4
2
 2   1  3  4
1-Hour: __Same_____
3-Hour: __Bethany___
Part D: Who would win if both girls running pace
were equal? Explain.
Time in hours
Answer: __If both girls kept the same
1  1
running pace, Calista would win because she
has a mile head start.______________________
Algebra 1: Systems Unit Review Answer Key
6/2/14
PUHSD Algebra Curriculum Team
III. F-LE.2 Learning Target: I can write a linear
function given a pattern, a set of ordered pairs, a
graph, or a slope and a point.
12. Write a system of equations represented by the
tables below.
Table A:
10. Write a system of equations represented by the
graph below.
x
y
-3
-1
1
2
3
11
5
-1
-4
-7
-2
-1
0
3
4
-6.5
-6.25
-6
-5.25
-5
Table B:
x
y
System: ___ y 
System: ___ y  3 x  2 ___
1
x  6 ____
2
___ y  0.25 x  6 ___
3
___ y   x  2 ___
2
13. Write a system of equations represented by the
tables below.
11. Part A: Graph a system that has the
solution (2, 4).
Table A:
x
-2
-1
1
2
3
Answers may vary, but an example…
y
1
2
4
5
6
Table B:
x
-3
0
1
2
3
y
12
6
4
2
0
Part B: Write the equations of the system that has
the solution (2, 4).
1
x  5 ___
2
System: ___ y  x  3 ____
___ y  x  2 ______
_ y   2 x  6 ___
System: ___ y  
Algebra 1: Systems Unit Review Answer Key
6/2/14
PUHSD Algebra Curriculum Team
14. You have $290 in savings and save an additional
$16 each week. Your brother has $430 in savings
and spends $12 of his savings each week. Write a
system of equations to represent the situation.
17. How many calories from problem #16 are in
each?
System: ___ S  16 w  290 ____
____ y   2 x  6 _____
15. After how many weeks from problem #14 will
you and your brother have the same amount of
savings and what amount of money will be in
Answer: _ The ice Cream has 130 calories and
each saving account when there the same?
the pie has 370 calories. _____________________
18. The manager of a movie theater wants to know
the number of adults and children who go to the
movies. The theater charges $8 for each adult
ticket and $4 for each child ticket. At a showing
where 200 tickets were sold, the theater collected
$1304. Write a system of equations to represent
the situation.
System: ___ 8a  4c  1304 __
____ a  c  200 ___
19. Find how many of each ticket from problem # 18
type were sold?
Answer: __It will take 5 weeks when you and your
brother will both have $370. __________________
16. The number of calories in a piece of pie is 20 less
than three times the number of calories in a scoop
of ice cream. The pie and ice cream together have
500 calories. Write a system of equations to
represent the situation.
System: ___ P  3 I  20 ___
___ P  I  500 ___
Algebra 1: Systems Unit Review Answer Key
Answer: _The movie theather sold 74 children
tickets and 126 adults tickets . _________________
6/2/14
PUHSD Algebra Curriculum Team
IV.
A-REI.12 Learning Target: I can graph the
solution to one or more liner inequalities.
21. Write a system of linear inequalities that defines
the shaded region.
System: ___ y  
1
x  2 ____
2
25. Mina’s Catering Services is organizing a formal
dinner for 280 people. The hall has two kinds of
table, one type of table seats 4 people and and
the other type of table seats 10 people. The hall
can contain up to a total of 52 tables. Write a
system of inequalities to represent the situation.
System: ___ x  y  52
____
__ 4 x  10 y  280
_____
26. Graph the system of inequalities to determine the
possiple combinations of tables that can be used
for the event so there are enough for all people.
___ y  x  1 ________
Mina’s Catering Service
22. Write a system of linear inequalities that defines
the shaded region.
y
72
10 people tables
64
56
48
40
32
24
System: ___ y   x ____
16
___ x  2 ___
8
24. Part A: Graph the linear system of inequalities.
3x  y  2

8 x  2 y  2
8
16
24
32
40
48
56
64
72
80 x
4 people tables
Answer:__ Mina’s Catering Services needs to use 40
Which of the following are solutions to the system?
a.
(2, 2)
b.
(0, 0)
c. (10, 1)
d. ( 4, 5)
tables that seat 4 people and 12 tables that seat 10
people in order to be able to seat all 280 people for
dinner._____________________________________
Algebra 1: Systems Unit Review Answer Key
6/2/14
PUHSD Algebra Curriculum Team