Question 1 Which of the following is the solution to system

| October 22, 2018

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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