Download ALG 03 - SYSTEMS Test Review File

Algebra
Test 3 Review
Name ____________________________
Instructor ______________ Hr/Blk __
Solve the following systems of equations using graphing.
Identify the system as consistent & independent, consistent & dependent, or inconsistent.
y = -3x + 4
y = 2x – 6
y = -2x + 2
2x + y = 2
5x + y = -5
10x + 2y = 10
3x – y = 0
y=x–2
Solve the following systems of equations using substitution.
Identify the system as consistent & independent, consistent & dependent, or inconsistent.
1. y = x + 3
y = –4x – 2
2. y = – 2x + 5
x + 3y = -5
3. x + 3y = 6
y = 2x – 5
4. 2x – y = 5
4x – 2y = 7
Solve the following systems of equations using elimination.
Identify the system as consistent & independent, consistent & dependent, or inconsistent.
1. x + y = 7
3x – 3y = 39
2. x – 3y = 27
x–y=3
3. 4x + 4y = -6
5x + 3y = 6
4. 2x – 8y = -16
5x – 20y = -40
Solve the following systems of equations using Cramer’s Rule.
1. x + 4y = 1
2x + 3y = 13
2. 3x + y = -8
4x – 2y = -14
3. 7x – 10y = -6
8y = 40
4. 4x – 2y = 15
5x + 3y = 7
Identify the system as consistent & independent, consistent & dependent, or inconsistent
and the number of solutions based on the determinants of Cramer’s Rule.
1. x 
? ?
? ?
? ?
? ?
? ?
? ?
2
3
 ,y 

0
0
? ?
? ?
2. x 
? ?
? ?
? ?
? ?
? ?
? ?
0
3
 ,y 

2
2
? ?
? ?
3. x 
? ?
? ?
? ?
? ?
? ?
? ?
0
0
 ,y 

0
? ? 0
? ?
Solve the following system
 x

2 x
 y
 3y
 4
 9
using …
… graphing
… substitution
… elimination
… Cramer’s Rule
Setup a system of equations and solve using any method.
1. A coin bank has 250 coins, dimes and quarters, worth $39.25. How many of each type of coin are there?
2. Admission for a charity square dance is $3 for adults and $1.50 for children. If 168 people attended the dance
and the money raised was $432, how many adults and how many children attended the dance?
3. I was able to purchase 1 paperback and 3 hardcovers for $24 at Vis’ Used Book Exchange. The next day I go
back and buy 5 paperbacks and 5 hardcovers for $50. What does Vis charge for paperbacks and hardcovers?
4. A soccer party serves subs sliced up in small sizes. My wife ate a total of two-thirds of a tuna sub and
1½ roast beef subs for a combined Calorie count of 800. I ate 2 6” tuna subs and four-fifth of a 6” roast beef
sub for a total of 1216 Calories. Determine the Calories of a roast beef sub and also a tuna sub.
Santiago has three job offers he is considering. Which job should he take to earn the max salary if he
works M months and earns the entire signing bonus? Be specific when considering different values of M.
How much Santiago would have earned for a year’s worth of work with bonus for each job?
 Buzzy Bee Biz pays $4800 per month.
 Coco Company pays him $4300 per month plus a signing bonus of $6000.
 Ink Inc. pays $3100 per month plus $600 per month toward his rent and a signing bonus of $12000.
Solve each system of inequalities using graphing.
1.
2.
y<5
x>4
3.
x < -2
y > 2x
4.
y > 2x – 3
1
y<  x+2
2
5.
3x – 2y > 6
2x – 4y > -4
6.
y>
2
x–4
5
y > –x + 1
y< 
1
x +3
6
x + 6y > -12
MULTIPLE CHOICE
_____ 1. Given the system of linear equations
Describe the graph of the system in the Cartesian (x, y) coordinate plane.
A. One line with negative slope
B. One line with positive slope
C. Two parallel lines with negative slope
D. Two parallel lines with positive slope
E. Two lines that intersect at a single point
12x  8y  24

 9x  6y   18
_____ 2. Given the system of linear equations
Describe the graph of the system in the Cartesian (x, y) coordinate plane.
A. One line with negative slope
B. One line with positive slope
C. Two parallel lines with negative slope
D. Two parallel lines with positive slope
E. Two lines that intersect at a single point
y  5 x  9

y   5 x  9
____
3. Identify the systems for questions #1 & #2
A. #1: consistent and dependent,
#2:
B. #1: inconsistent,
#2:
C. #1: consistent and independent, #2:
D. #1: inconsistent,
#2:
E. #1: consistent and dependent,
#2:
inconsistent
consistent and independent
consistent and dependent
consistent and dependent
consistent and independent
_____ 4. You and your friend take advantage of a store promotion. For $39, you bought 5 DVD and 4 Blu-Ray movies.
Your friend spends $39 on 1 DVD and 6 Blu-Ray movies. If all of the DVDs purchased were one set price and
all of the Blu-Rays were one set price, how much was one Blu-Ray?
A. $2
B. $3
C. $4
D. $5
E. $6
_____ 5. Which of the following expressions is being graphed above?
4
A. y > x + 5
5
5
B. y > x + 4
4
4
C. y < x – 4
5
D. 4x + 5y > 20
E. 5x + 4y < 9
_____ 6. You solved a linear system with two equations and two variables and got the equation 4 = 4
How many solutions does the system of equations have?
A. no solution
B. exactly 1 solution
C. exactly 2 solutions
D. exactly 4 solutons
E. infinitely many solutions
_____ 7. The sum of two numbers is 12. The difference of the same two numbers is -4.
What is the smaller of the two numbers?
A. 4
B. 5
C. 6
D. 7
E. 8
_____ 8. Which of the following setups would be used to solve the following problems?
A test has twenty-five questions worth 100 points. The test consists of multiple choice questions worth 3 points
each and free-response questions worth 8 points each. How many multiple choice questions are on the test?
A. m + 8f = 100,
m + 3f = 25
(m = # of multiple choice, f = # of free response)
B. m + f = 25,
8m + 3f = 100
C. m + f = 100,
3m + 8f = 25
D. 3m + f = 25,
m + 8f = 108
E. none of the above
_____ 9. What do both dependent systems and inconsistent systems have in common?
A. no solution
B. same slope
C. same y-intercept
D. same slope and y-intercept
E. different slope, different y-intercept
_____ 10. What is the approximate solution of the linear system
represented by the graph at the right?
A. (0, 2)
D. (1, 1)
B. (3, 0)
E. (4, 3)
C. (0, -7)
_____ 11. Which of the following setups is correct
for solving x for the following system
using Cramer’s Rule?
A.
7
0
6 8
13
0
 20  8
B.
13
0
 20  8
7
13
6  20
7x  y  13

6x  8y   20
C.
7
13
6  20
7
0
6 8
D.
13
1
 20  8
7
1
6 8
E.
7
13
6  20
13
1
 20  8
_____ 12. Which of the following setups would be used to solve the following problems?
A restaurant contains both two-seat booths and four-seat tables. The number of booths and tables
combined is 17. The maximum occupancy of the restaurant is 56. How many four-seat tables are there?
A. b + t = 17, b + t = 56
(b = # of booths, t = # of tables)
B. 2b + 4t = 17, b + t = 56
C. b + t = 17, 2b + 4t = 56
D. 2b + 4t = 17, 2b + 4t = 56
E. none of the above
_____ 13. In the Cartesian (x, y) coordinate plane, find the x-coordinate of the point
where y = 4x + 4 and y = 7x – 5 intersect.
A. -1
B. 11
C. 2
D. 16
E. 3
_____ 14. You solved a linear system with two equations and two variables and got the equation 3 = -5
How many solutions does the system of equations have?
A. no solution
B. exactly 1 solution
C. exactly 3 solutions
D. exactly 5 solutions
E. infinitely many solutions
_____ 15. The perimeter of a rectangle is 24 in. and its length l is 3 times the width w.
What is the length and width (l, w) of the rectangle?
A. (3, 9)
B. (14.4, 4.8)
C. (12, 4)
D. (9, 3)
E. (18, 6)
_____ 16. The shaded region of the graph represents
which system of inequalities?
A. y < -x + 5 AND y < 2x – 1
B. y < -x + 5 AND y > 2x – 1
C. y > -x + 5 AND y < 2x – 1
D. y < -x + 5 OR y > 2x – 1
E. y > -x + 5 OR y < 2x – 1
_____ 17. Evaluate the determinant:
A.
B.
C.
D.
E.
-31
-14
-1
1
31
2 3
5
8