Give a real-life situation or application problem using a system of equations that shows how powerful algebra is.In other words, it would be almost impossible or very complicated to figure out the solutions without such a tool.

1.Determine if (7, 6) is a solution of the system

2x - 3y = -4

2x + y = 4.

Select one:

A. Yes

B. No

C. Can't determine

Question 2

Solve the system

x + y = 6

3x - y = 6.

Select one:

A. (1, -3)

B. (3, 3)

C. (-3, 9)

D. (2, 0)

Question 3

Solve the system

y = 3x - 10

y = 3x + 1

Select one:

A. (1, -7)

B. (1, 4)

C. (2, -4)

D. No solution

Question 4

Solve the system

3x - 6y = 12

x - 2y = 4

Select one:

A. (2, -1)

B. (4, 0)

C. No solution

D. Infinitely many solutions

Question 5

When solving the system

5x - 4y = 9

x - 2y = -3,

what is the best first step?

Select one:

A. Rewrite the second equation as x = 2y - 3.

B. Rewrite the second equation as y = (1/2)x + 3/2

C. Rewrite the first equation as x = (4/5)y + 9/5

D. Rewrite the first equation as y = (5/4)y - 9/4

Question 6

Solve the system

5x - 4y = 9

x - 2y = -3.

Select one:

A. (1, -1)

B. (4, 5)

C. (5, 4)

D. No solution

Question 7

Solve the system

2x - y = 6

3x + 2y = 5

Select one:

A. (4, 2)

B. (17/7, -8/7)

C. (17, -8)

D. No solution

Question 8

Solve the system

y = (-1/2)x + 2

y = (3/4)x + 7.

Select one:

A. (-4, 4)

B. (-1/2, 3/4)

C. (0, 2)

D. No solution

Question 9

When using the addition method to solve the system

4x - y = 22

3x + 4y = 26,

what is the first best step?

Select one:

A. Add the first equation to the second equation.

B. Multiply 4 to each of the first equation and add the equations.

C. Multiply -4 to each of the first equation and add the equations.

D. Multiply 3 to each of the first equation and 4 to each of the second equation and add them.

Question 10

Solve the system

4x - y = 22

3x + 4y = 26.

Select one:

A. (8, 0)

B. (5, -2)

C. (6, 2)

D. No solution

Question 11

Solve the system

7x - 4y = 13

-7x + 6y = -11.

Select one:

A. (1, -3/2)

B. (17/7, 1)

C. (1, 2/3)

D. No solution

Question 12

Solve the system

4x - y = 22

-4x + y = 26.

Select one:

A. (5, -2)

B. (-5, 6)

C. (7/25, -1/25)

D. No solution

Question 13

Solve the system

2x - y = 3

4x + 4y = -1.

Select one:

A. (11/12, -7/6)

B. (11/12, 7/6)

C. (33/16, 3/8)

D. No solution

Question 14

Consider the following problem:

A rectangular lot whose perimeter is 1600 feet is fenced along three sides. An expensive fencing along the lot's length costs $20 per foot. An inexpensive fencing along the two side widths costs only $5 per foot. The total cost of the fencing along the three sides comes to $13,000. What are the lot's dimensions? You need not solve the problem.

If x is the length of the expensive side and y is the length of an inexpensive side, what is the algebraic expression for the statement "A rectangular lot whose perimeter is 1600 feet is fenced along three sides?"

Select one:

A. x + y = 1600

B. 2x + 2y = 1600

C. x + 2y = 1600

D. 2x + y = 1600

Question 15

Refer to Question 14):

Consider the following problem:

A rectangular lot whose perimeter is 1600 feet is fenced along three sides. An expensive fencing along the lot's length costs $20 per foot. An inexpensive fencing along the two side widths costs only $5 per foot. The total cost of the fencing along the three sides comes to $13,000. What are the lot's dimensions?

What is the algebraic expression for the statement "The total cost of the fencing along the three sides comes to $13,000?"

Select one:

A. 20x + 5y = 13000

B. x + y = 13000

C. 5x + 20y = 13000

D. 20x + 10y = 13000