Determine the values of aa and bb such that the system of linear equations has infinitely many solutions:
ax + by = 3
2x + y = 1

A) a = 6 , b = 3

B) a = 6, b = 6

C) a = 3, b = 6

D) a = 3, b = 3

Emma and David are selling lemonade for a fundraiser. They started with the same amount of lemonade mix, but Emma added 2 cups of water to her mix, while David said 4 cups. After selling some lemonade, Emma’s mixture has 8 cups of liquid, while David’s has 10 cups of liquid.

A) 8 cups

B) 6 cups

C) 10 cups

D) 4 cups

Which of the following system of equations has an infinite number of solutions?

A) x = - 5
y = 10

B) x = 10y
y = 10x

C) \$y = 1/2 x + 5\$
4y = 2x + 20

D) y = - 4x - 10
y = - 4x - 15

A gardener plants flowers in a rectangular garden. The total number of flowers planted is 300. If she plants 15 rows of daisies and 10 rows of tulips, she uses 300 flowers. If she plants 10 rows of daisies and 15 rows of tulips, she also uses 300 flowers. Find the number of daisies and tulips planted in each row.

A) 18

B) 21

C) 24

D) 12

Samantha has some $20 bills and $10 bills. She has a total of 12 bills with a combined value of $200. How many $20 bills and $10 bills does she have?

A) (4, 4)

B) (8, 8)

C) (4, 5)

D) (8, 4)

For what values of a and b does the following system of linear equations have infinitely many solutions?
ax + by = 1
(a + b)x + (a + 2b)y = 2

A) a ≠ 1 and b ≠ 1

B) a = 0 and b ≠ 2

C) a = 0 and b ≠ 0

D) a = 1 and b ≠ 0

A movie theater offers tickets for adults (A) and children © at different prices. A group of friends wants to buy a total of 12 tickets. They know that 3 adults and 4 children cost the same amount as 2 adults and 6 children. Write down a system of equations representing this scenario and find the values for which there are infinitely many solutions.

A) A = 12, C = 0

B) A = 8, C = 4

C) A = 6, C = 6

D) A = 4, C = 8

Determine the values of k for which the system of linear equations has infinitely many solutions:
2x + 3y = 5
4x + ky = 10

A) k = 6

B) k = 2

C) k = 0

D) k = 8

A pet shop sells two types of food packages for dogs. Package A costs $20 and Package B costs $30. A customer wants to spend no more than $100 on dog food and needs at least 4 packages. Write a system of equations to represent this situation

A) 20x + 30y ≥ 100, x + y ≥ 4

B) 20x + 30y ≤ 100, x + y ≥ 4

C) 20x + 30y ≤ 100, x + y ≤ 4

D) 20x + 30y ≥ 100, x + y ≤ 4

Analyze the following system to find the conditions under which it has infinite solutions:
​2x − y + 3z = 7
4x − 2y + 6z = 14
6x − 3y + mz = 21​

A) m = 7

B) m = 8

C) m = 9

D) m = 10