Ch 8 Review
Note: These are only a sample of the type of problems you may see on the exam.
Determine whether the ordered pair is a solution of the
Identify the system as consistent or inconsistent, and
system of equations.
dependent or independent.
1) (3, 5); y = 3x + -12
5) x + 6y = 20
7x - y = 16
2x + 12y = 40
Answer: No
Determine whether the ordered pair is a solution of the
system of equations. Remember to use alphabetical order
of variables.
2) (-3, -1); x - y = -2
y = 9x + 26
Answer: Yes
Solve the system graphically. Be sure to clearly state the
solution(s). Also, classify the system as being
independent/dependent and consistent/inconsistent.
3) y =-6 + 3x
x -3y = -6
Answer: Consistent and dependent
6) 3x = y + 3
6x - 2y = 3
Answer: Inconsistent and independent
Solve using the substitution method. Be sure to clearly
state the solution(s).
7) 3x + y = 13
2x + 9y = -8
Answer: (5, -2)
Solve using the substitution method. If the system has an
infinite number of solutions, use set-builder notation to
write the solution set. If the system has no solution, state
this.
8) 3y + x = -7
x = 4y + 9
1
16
1
16
A) , B) - , 7
7
7
7
C)
1 16
,
7 7
D) -
1 16
,
7 7
Answer: B
Answer: (-3, -6)
Solve the system graphically. If the system has an infinite
number of solutions, use set-builder notation to write the
solution set. If the system has no solution, state this.
4) x = y - 3
3x = 2y
Solve using the elimination method. Be sure to clearly
state the solution(s). Also, classify the system as being
independent/dependent and consistent/inconsistent.
9) 3x - 4 = y
y - 3x = 3
Answer: No solution
Solve using the elimination method. If the system has an
infinite number of solutions, use set-builder notation to
write the solution set. If the system has no solution, state
this.
10) x + 3y = 29
-6x + 2y = -34
Answer: (8, 7)
11) 3r - 3s = 2
-3r + 3s = 2
Answer: No solution
Answer: (6, 9)
Solve using any appropriate method. Be sure to clearly
state the solution(s). Also, classify the system as being
independent/dependent and consistent/inconsistent.
12) 3x + 5y = -2
-6x - 10y = 4
Answer: {(x, y)|3x + 5y = -2}
Solve using any appropriate method. If the system has an
infinite number of solutions, use set-builder notation to
write the solution set. If the system has no solution, state
this.
13) 7x - 4y = 0
6x + 6y = 66
Answer: (4, 7)
Solve using any appropriate method. Be sure to clearly
state the solution(s).
14) 4x + 8y = 40
5x + 4y = 8
Answer: (-4, 7)
Solve the problem.
15) The sum of two numbers is 32, and their
difference is 12. What are the numbers?
Answer: 10, 22
16) Two angles are complementary. The sum of
the first angle plus twice the second angle is
148°. Find the measures of the angles.
Answer: 32°, 58°
17) The speed of a current is 6 mph. If a boat
travels 52 miles downstream in the same time
that it takes to travel 26 miles upstream, what
is the speed of the boat in still water?
Answer: 18 mph