Chapter 5 Test—Algebra I
Name ________________________
I Write the letter for the correct answer in the blank at the right of each problem. (4 points each).
See the graphs below to answer questions #1,#2,#3, and #7.
1. Which ordered pair is the solution of the system of equations represented by lines q and s?
a. ( 0 , 2 )
b. ( 2 , 4 )
c. ( 1 , -1 )
d. ( -1 , 1 )
1. _______
2. How many solutions are there of the system of equations represented by line q and y = -x?
a. exactly one
b. exactly two
c. no solutions
d. infinitely many
2. _______
3. How many solutions are there of the system of equations represented by line q and p?
a. exactly one
b. exactly two
c. no solutions
d. infinitely many
3. _______
4. If the system of equations 3x + y = 14 and x + 4y = 3 is to be solved by substitution, which
expression can be substituted for y in the equation?
a. 3 – 4y
b. 14 – 3x
c. (14 – y )/3
d. (3 – x)/4
4. _______
5. If the system 3x + 5y = 16 and 8x – 5y = 28 is solved by elimination, what is the value of x?
a. 4
b. 5
c. -6
d. 7
5. ________
6. If the system 2x – 5y = 1 and -3x + 7y = -3 is to be solved by elimination of the variable x,
and the first equation is multiplied by 3, then by which number should the second equation be
multiplied?
a. 3
b. 5
c. -3
d. 2
6. ________
7. Which point is a solution to the system of equations in the graph?
a. ( 2 , 1 )
b. ( -3 , -1 )
c. ( -1 , -1 )
d. ( -2 , 3 )
7. ________
8. Is this system said to be __________________
a. consistent and independent
b. consistent and dependant
Use for question #1 - #3
c. inconsistent
8. ________
Use for question #7 - #8
II. Solve each system by using the specified method. Show your work and express the solution as an ordered
pair. (6 points each).
1. Solve the system of equations x + 3y =12 and x – 3y = -6 by graphing.
2. Solve the system 3x – y = 4 and 2x – 3y = -9 by substitution.
3. Solve the system 2x + 5y = 7 and 3x + 6y = 3 by elimination.
4. Solve the system 2x + 2y =3 and x – 2y = 1 by any method.
III. Graphing Calculator. Solve the system of equation by graphing. (10points ).
1. Two planes are in flight near a local airport. One plane is at an altitude of 1,000 meters and is ascending at a rate
of 400 meters per minute. The second plane is at an altitude of 5,900 meters and is descending at a rate of 300
meters per minute.
Write a system of equations that represents the progress of each plane.
Y = ____________________
and
Y = _______________________
Approximately when will the planes be at the same elevation?
X = __________ minutes
and
Y = ______________ elevation
What window settings did you use?
X min = _______
X max = ________
Y min = _______
Y max = _______
IV. Define two variables, write a system of equations, and then solve. (7 points each).
1. There are 812 students in a school. There are 36 more girls than boys. How many girls are there?
2. The length of a rectangle is 20 cm. greater than its width. The perimeter is 360 cm. What are the dimensions of
the rectangle? What is the area of the rectangle?
Bonus. Solve on the back. A farmer replied that his dogs and chickens have a total of 148 legs and 60 heads. How
many of each animal does the farmer have? (Solve using algebraic methods)