### Algebra 1 – Systems of Equations Review Name: Pd: ____ 1

```Algebra 1 – Systems of Equations Review
Name: ______________________ Pd: ____
1) Roberto buys a popcorn and medium soda from the concession stand at Regal
Cinemas for \$9.00. Josh buys 1 popcorn and 2 medium sodas for \$12. What is
the cost of the bag of popcorn?
(1) \$6.00
(2) \$4.50
(3) \$3.00
Ans: ____
(4) \$5.00
 y  2x  3

2) Which of the following points is the solution to the system 
?
1
y


x

2

2
(1) (1,5)
(2) (2,-4)
(3) (-2,-1)
(4) (1,4)
3) Which ordered pair is in the solution set of the following system of inequalities?
Ans: ____
Ans: ____
y > 2x – 3
y < -x + 3
(1) (0, -3)
(2) (0, 0)
(3) (2, 1)
(4) (3, 5)
4) What is the value of the y-coordinate of the solution to the system of equations
2x + 3y = 4 and -x + 3y = -11?
(1) -2
(2) 5
(3) 3
Ans: ____
(4) -6
2 x  2 y  16
5) Which system of equations has the same solution as the system 
3 x  y  4
2 x  2 y  16
 x  y  16
(1) 
(3) 
6 x  2 y  4
3 x  y  4
2 x  2 y  16
6 x  6 y  48
(2) 
(4) 
6 x  2 y  8
6 x  2 y  8
Ans: ____
6) A gas truck is filling the underground storage tanks at a gas station. Currently, the
storage tank has 150 gallons of gas and truck has 2,530 gallons of gas. The truck
is pumping into the storage tank at a rate of 35 gallons per minute. How long until
the volumes of the truck and the storage tank are equal?
(1) Never
(2) 34 minutes
(3) 38 minutes
Ans: ____
(4) 68 minutes
7) On the set of axes below, graph the following system of inequalities and state the coordinates of a point
in the solution set.
3y > 6x – 3
y < -x + 6
A point in the solution set: _________
8) On the grid below, solve the system of equations graphically for x and y.
4y – 5x = -4
2y = -x – 2
Solution set: ____________
Check
9) Solve the following systems of equations algebraically
x  3y  4

3 x  3 y  6
CHECK
10) The cost of 2 folders and 5 pens at a particular school store is \$6.75. The cost of 5 folders and 1 pen is
\$8.25. What is the cost of each item? Include appropriate units in your answer.
11) While bored, the cashier at a convenience store counts the coins in the coin tray by the register. He
finds that there are 22 pennies and dimes, totaling 58 cents. How many pennies did he count?
Honors Review
Johnson's Produce is purchasing fertilizer with two nutrients: Nitrogen and Phosphorus. They need at least
90 pounds of phosphorus, and state law says they can buy no more than 180 pounds of nitrogen in a single
order. Their supplier has two brands of fertilizer available. Brand X has four pounds of nitrogen and one
pound of phosphorus per bag. Brand Y has one pound of each nutrient.
a) Write a system of inequalities that models the situation above.
b) If Johnson’s Produce got 15 bags of Brand X, between how many bags of Brand Y could they legally
purchase and still meet their minimum phosphorus need?
Number of bags of Brand Y
c) Graph the system on the axes below.
Number of bags of Brand X
d) What is the largest number of bags of Brand X Johnson’s Produce could buy to meet their need and still
abide by the law?
```