Question 1 Which of the following is the solution to system
Question 1
Which of the following is the
solution to system
3x + 4y = 7
x + 2y = 2
Answer

(x = 6, y = 2) 


(x = 5, y = 2) 


(x = 4, y = 1/2) 


(x = 3, y = 1/2) 
Question 2
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution.
2x 3y =2
6x 9y =8
Answer

one solution 


infinitely many solutions 


no solution 


can not tell 
10 points
Question 3
Solve the linear system of equations x +4y =9, 0.5x + 2y = 4.5.
Answer

Unique solution: (1, 2) 


Unique solution (4, 1 ) 


Infinitely many solutions; (94k, k) 


No solution. 
10 points
Question 4
A farmer has 400 acres
available for cultivating crops A and B. He has a maximum of 13,200 hours
of labor available. The labor required for cultivation crop A is 20 hours
per acre and for crop B is 30 hours per acre.
Write the system of equations needed to determine how many acres of each crop
should the farmer plant if he wishes to utilize all his resources.
(Let x = number of acres for cultivating crop A, y = number of acres for
cultivating crop B).
Answer

x+y = 400 


x+30y= 400 


x+y= 400 


none of the above 
10 points
Question 5
A restaurant manager wants to purchase 200 sets of dishes. One design costs $25 per set, while another costs $45 per set. If she only has $7400 to spend, how many of each design should be ordered?
Answer

110 $25 sets and 90 $45 sets 


100 $25 sets and 100 $45 sets 


120 $25 sets and 80 $45 sets 


80 $25 sets and 120 $45 sets 
10 points
Question 6
Determine the value of k for which the system of linear equations has no solution.
2x y = 3,
4x + ky = 5
Answer

2 


5/3 


2 


4 
10 points
Question 7
Write the augmented matrix corresponding to the given system of equations.
2x  3y =4
3x  2y =5
Answer

[2 3] [3 2] 


[2 3] [32] 


[234] [325] 


[423] [532] 
10 points
Question 8
Which of the followings is not in row reduced form?
Answer

[102] [003] 


[102] [013] 


[1201] [0013] [0000] 


[1100] [0100] [0000] 
10 points
Question 9
Given matrix
[1231]
[2112]
[1057]
What will be the new second row after the row operation: R22R1+R3?
Answer

[0, 3, 7 4] 


[1, 3, 2  11] 


[1, 1, 4  9] 


[0, 0, 1  2] 
10 points
Question 10
With GaussJordan elimination, the following matrix can be reduced to the reduced form
[123]
[234]
Answer

[123] [012] 


[101] [012] 


[101] [111] 


[111] [012] 

Rating:
5/
Solution: Question 1 Which of the following is the solution to system