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]