Sarah plans to buy apples and oranges from two different vendors. Vendor A sells apples for $1 each and oranges for $2 each, while Vendor B sells apples for $2 each and oranges for $1 each. Sarah wants to buy 5 fruits and spend exactly $7. How many apples and oranges should she buy from each vendor?

A) 2 apples from Vendor A and 3 oranges from Vendor B

B) 4 apples from Vendor A and 1 orange from Vendor B

C) 3 apples from Vendor A and 2 oranges from Vendor B

D) 1 apple from Vendor A and 4 oranges from Vendor B

Solve the following systems using substitution. If there is no unique solution, state whether there is no solution or infinitely many solutions.
- x + 7y = 5
3x - 21y = - 5

A) - 15 = 5

B) 10 ≠ 5

C) - 10 = - 5

D) - 15 ≠ - 5

A charity organization sells two types of merchandise: T-shirts and hats. Each T-shirt costs $15 and each hat costs $10. The organization conducted a fundraiser where they sold a total of 100 items and raised $1200. However, they discovered later that the number of hats sold was incorrectly reported. They realized that the number of T-shirts sold was twice the number of hats sold. Determine the number of T-shirts and hats sold during the fundraiser.

A) 23.33

B) 33.33

C) 43.33

D) 53.33

Which of the following systems of linear equations has no solution?

A) y = 6x + 3, y = 6x + 9

B) y = 10, y = 10x + 10

C) y = 14x + 14, y = 10x + 14

D) x = 3, y = 10

Find the value of m for which the system has no solutions:
2x + my = 6
4x + 2y = 12

A) m = 5

B) m = 7

C) m = 6

D) m = 8

Which of the following statements is true about the system:
2x - 3y = 5
4x + 6y = 10

A) The system has infinitely many solutions.

B) The system has no solutions.

C) The system has a unique solution.

D) The system is inconsistent.

A bookstore is comparing the prices set by two different suppliers for two types of books: novels and textbooks. Supplier X offers novels for $5 each and textbooks for $10 each. Supplier Y offers novels for $7 each and textbooks for $14 each. The bookstore finds out that the total price of buying 3 novels and 2 textbooks from Supplier X is the same as buying 3 novels and 2 textbooks from Supplier Y. Determine if there is a pricing inconsistency.

A) - 35 = - 49

B) 35 ≠ 49

C) - 35 ≠ - 49

D) - 35 = 49

Which of the following systems has no solutions?

A) x + 2y = 5
2x + 4y = 10

B) x + 2y = 3
2x + 4y = 6

C) x + 2y = 5
2x + 4y = 8

D) x + 2y = 10
2x + 4y = 20

Determine the condition under which the system has no solutions:
3x + 2y = 8
6x + 4y = k

A) k = 6

B) k = 8

C) k = 10

D) k = 12

A farm produces two types of fertilizers: Fertilizer A and Fertilizer B. The farm has a total of 100 pounds of fertilizer. Fertilizer A contains 30% nitrogen and 70% phosphorus, while Fertilizer B contains 50% nitrogen and 50% phosphorus. If the farm wants to have a total of 40 pounds of nitrogen, how many pounds of each type of fertilizer should they use?

A) A = 50 pounds and B = 60 pounds

B) A = 60 pounds and B = 50 pounds

C) A = 45 pounds and B = 55 pounds

D) A = 50 pounds and B = 50 pounds