Download Ch 8 Exam Review Note: These are only a sample of the type of

Ch 8 Exam Review
Note: These are only a sample of the type of problems you may see on the test. Anything covered in class or homework
may appear on the test.
Identify the system as consistent or inconsistent, and
Determine whether the ordered pair is a solution of the
system of equations. Remember to use alphabetical order
dependent or independent.
5) x + 6y = 20
of variables.
2x + 12y = 40
6x + y = 17
1) (3, -1);
2x - 3y = 9
Answer: Consistent and dependent
Answer: Yes
6) 3x = y + 3
6x - 2y = 3
2) (5, -5); -2a - 5b = 15
6a + 15b = -45
Answer: Inconsistent and independent
Answer: Yes
7) -8x + 2y = -6
-4x - y = -3
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.
3) x - y = 2
x + y = 14
Answer: Consistent and independent
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) 5x - 2y = -1
x + 4y = 35
Answer: (3, 8)
9) 3y + x = -7
x = 4y + 9
Answer: -
1
16
,7
7
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 + 2y = -13
2x + 2y = -14
Answer: (8, 6)
4) x = y - 3
3x = 2y
Answer: (-1, -6)
11) -7x + 8y = 64
-4x - 4y = -32
Answer: (0, 8)
12)
1
1
x- y=3
3
4
2
1
x+ y=1
3
2
Answer: (6, 9)
Answer:
1
21
, -5
4
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) 0.1x + 0.5y = 2
0.5x - 0.1y = 1
20) Determine whether (-3, -1, 4) is a solution of
the system
2x - 2y - 3z = -16
4x - 3y + 3z = 3
x + y - 5z = -24.
Answer: Yes
35 45
,
Answer:
13 13
21) Determine whether 6, -
11
, -4 is a solution of
2
the system
3x - 2y + 3z = 17
x + 4y - 2z = -8
2x - y + z = 8.
Solve the problem.
14) The sum of two numbers is 112. The second
number is three times as large as the first
number. What are the numbers?
Answer: 28, 84
Answer: No
15) Two angles are supplementary. One angle is
212° less than three times the other. Find the
measures of the angles.
Solve the system. Be sure to know all mehods!
22) x - y + z = -4
x + y + z = -2
x + y - z = -6
Answer: 98°, 82°
Answer: (-5, 1, 2)
16) 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?
23) 9x - 9y - 6z = -11
6x + 3y - 3z = 1
x - y + 2z = -3
Answer: 18 mph
Answer: -
17) Don runs a charity fruit sale, selling boxes of
oranges for $11 and boxes of grapefruit for $10.
If he sold a total of 762 boxes and took in $8125
in all, then how many boxes of oranges did he
sell?
2
2
, 1, 3
3
24) -4x - y + 9z = 37
-9x
+ 7z = -7
5y + z = 43
Answer: (7, 7, 8)
Answer: 505 boxes
25) 3x - 4y = -3
7
6x + 2z = 2
18) A contractor mixes concrete from bags of
pre-mix for small jobs. How many bags with
5% cement should he mix with 4 bags of 13.5%
cement to produce a mix containing 7%
cement?
2y - 4z = 4
Answer: -
Answer: 13 bags
1 1
3
, ,3 2
4
Solve the system. If the system's equations are dependent
or if there is no solution, state this.
26) 2x + 8y + 4z = 0
x + 4y + 2z = -28
x + y + z = -4
19) Mardi received an inheritance of $60,000. She
invested part at 10% and deposited the
remainder in tax-free bonds at 12%. Her total
annual income from the investments was
$6400. Find the amount invested at 10%.
Answer: No solution
Answer: $40,000
27) -3x - 4y + 2z = 25
12x + 16y - 8z = -100
-9x - 12y + 6z = 75
Answer: The equations are dependent.
2
Solve.
28) The sum of a student's three scores is 221. The
first is 20 more than the second, and the sum of
the first two is 8 more than twice the third.
Find the student's first score.
Answer: 85
29) Michael's bank contains only nickels, dimes,
and quarters. There are 66 coins in all, valued
at $5.35. The number of nickels is 2 short of
being three times the sum of the number of
dimes and quarters together. How many dimes
are in the bank?
Answer: 9
Evaluate.
30)
42
53
Answer: 2
31)
-1 1
33
Answer: -6
32)
-1 -3 -3
4
-5
5 -1
2
3
Answer: -95
33)
5 2 5
5 1 2
5 1 1
Answer: 5
Solve using Cramer's rule.
34) -2x - 2y = -18
3x + 5y = 43
Answer: (1, 8)
35) 2x + 2y = 28
2x - 3y = -2
Answer: (8, 6)
3