# 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;

(9-4k, 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

20x+30y=13200

x+30y= 400

x+20y =13200

x+y= 400

20x+4z=11200

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]

[-3-2]

[2-34]

[3-25]

[42-3]

[53-2]

10 points

Question 8

Which of the followings

is not in row reduced form?

Answer

[10|2]

[00|3]

[10|2]

[01|3]

[120|1]

[001|3]

[000|0]

[110|0]

[010|0]

[000|0]

10 points

Question 9

Given matrix

[123|-1]

[21-1|2]

[-105|7]

What will be the new second row after the row

operation: R2-2R1+R3?

Answer

[0, -3, -7 |4]

[-1, -3, -2 | 11]

[1, 1, 4 | 9]

[0, 0, 1 | 2]

10 points

Question 10

With Gauss-Jordan

elimination, the following matrix can be reduced to the reduced form

[12|3]

[23|4]

Answer

[12|3]

[0-1|-2]

[10|-1]

[01|2]

[10|-1]

[11|1]

[11|1]

[01|2]

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