Name__________________________________________
ALGEBRA
1) Which ordered pair is in the solution set of the
following system of linear inequalities?
1)
2)
3)
4)
2) Which point lies on the line whose equation is
?
Date______________________________
REVIEW FOR SYSTEMS TEST
5) Which system of equations would have the same
solution as the system:
x y 5
3 x  2 y  10
1)
3x  2 y  5
x  y  10
3)
 3x  3 y  5
3 x  2 y  10
2)
4)
 3 x  3 y  15
3x  2 y  10
2x  2 y  5
3 x  2 y  10
1)
2)
3)
4)
3) When using the substitution method, which of the
following equations could be used?
x  5 y  7
6) Which coordinate point is in the solution set for
the system of inequalities shown in the
accompanying graph?
4 x  5 y  17
1)
2)
3)
4)
4(5 y  7)  5 y  17
4 x  5(5 y  7)  17
4 x  5(5 y  7)  17
4(5 y  7)  5 y  17
(1)
(2)
(3)
(4)
(3,1)
(1,-1)
(2,2)
(0,1)
4) The set of equations x+2y=4 and 2x+4y=10 has 7) When solved graphically, which system of
____________.
equations will have exactly one point of intersection?
1)
1) an infinite number of solutions
2) one solution
2)
3) no solution
4) two solutions
3)
4)
8) The value of the x-intercept for the graph of
2 x  4 y  16 is
1) 0
2) 4
3) 8
4) -2
On
9) The Class of 2015 is running a bake sale as a
fundraiser. On the first day, a total of 40 items were
sold for $356. If pies, p, cost $10 and cakes, c, cost
$8, which system of equations would be used to find
the number of pies and cakes sold?
1)
p  c  40
8 p  10c  356
3)
p  c  40
8 p  10c  356
2)
p  c  40
10 p  8c  356
4)
p  c  40
10 p  8c  356
10) On the axes below, graph the following system of inequalities. Label your solution set with S.
x y 4
x4
11) Katie makes $7 an hour working at the grocery store and $10 an hour delivery newspapers. She
cannot work more than 20 hours per week. Katie wants to earn at least $150 per week.
Define the variables, and write a system of inequalities to represent the situation.
If Katie works 5 hours delivering newspapers, will she reach her goal of earning $150 per week while
working no more than 20 hours per week? Justify your response.
12) The owner of a movie theater was counting money from 1 day’s ticket sales. He knew that a total of 150
tickets were sold. Adult tickets cost $7.50 each and children’s tickets cost $4.75 each. If the total receipts for
the day were $891.25, how many of each kind of ticket were sold?
13) Alexandra purchases two doughnuts and three cookies at a doughnut shop and is charged $3.30. Brianna purchases
five doughnuts and two cookies at the same shop for $4.95. All the doughnuts have the same price and all the cookies
have the same price. How much money is needed to buy a combination of one doughnut and one cookie?
14) You are looking to join a monthly coffee delivery club. Your search has been narrowed down to the two top rated
clubs on the Internet. Five Star Coffee charges $55 start up fee and then $8 per month. Custom Coffee Company charges a
$25 start up fee and $12.50 per month.
a. Write an equation for the total cost, y, for each coffee company after x months.
b. How do the different monthly fees affect the graphs of the lines?
c. When will it be less expensive to be a member of Five Star Coffee?
Total Cost
Months
15) A high school drama club is putting on their annual theater production. There is a maximum of 800
tickets for the show. The costs of the tickets are $6 before the day of the show and $9 on the day of the
show. To meet the expenses of the show, the club must sell at least $5,000 worth of tickets.
a) Write a system of inequalities that represent this situation.
b) The club sells 440 tickets before the day of the show. Is it possible to sell enough additional
tickets on the day of the show to at least meet the expenses of the show? Justify your answer.
16) Mo's farm stand sold a total of 165 pounds of apples and peaches. She sold apples for $1.75 per pound and
peaches for $2.50 per pound. If she made $337.50, how many pounds of peaches did she sell?
1) 11
2) 18
3) 65
4) 100
17) Albert says that the two systems of equations shown below have the same solutions.
Determine and state whether you agree with Albert. Justify your answer.
18) Alicia has invented a new app for smart phones that two companies are interested in purchasing for a 2-year
contract. Company A is offering her $10,000 for the first month and will increase the amount each month by
$5000. Company B is offering $500 for the first month and will double their payment each month from the
previous month. Monthly payments are made at the end of each month. For which monthly payment will
company B’s payment first exceed company A’s payment?
1) 6
2) 7
3) 8
4) 9