Linear Inequalities in Two Variables

In order to raise money to attend upcoming competitions, the debate team at Lancaster High School is selling apple cider and hot chocolate at a basketball game. They hope to make at least $170 in revenue at tonight's game, with hot chocolate, x, selling for $1 and hot apple cider, y, selling for $2.

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

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A grill at a barbecue restaurant will be used to cook sausage links that are 2 lb each and briskets that are 6 lb each. No more than 120 lb of sausage links and briskets will be cooked on the grill.<\/p>

Which inequality represents all possible combinations of x<\/em>, the number of sausage links that will be cooked on the grill, and y<\/em>, the number of briskets that will also be cooked?<\/p>

Sophia and Benjamin are playing a game where they need to find if a point lies within a certain region defined by an inequality. They are currently looking at the inequality 6x+2y ≤ -8. Arjun suggests the point (-2,2). Is Arjun's point a solution to the inequality?

• Yes

• No

Determine if the point (0, 0) is a solution to the following system.
x - y < 2
x + y < 2
x ≥ -2

• Yes

• No

Which of the following ordered pairs does not solve the inequality?

• (9,-5)

• (3,-4)

• (-9,3)

• (-3,-3)

Which of the following is not a solution to the inequality x + 3y < 6 ?

• A. (2,3)

• B. (1,1)

• C. (4,0)

• D. (-2,-1)

Which of the following inequality has (5, 1) as a solution?

• 3𝑥 + 𝑦 ≤ 3

• 3𝑥 – 𝑦 ≤ 3

• 3𝑥 – 𝑦 < 15

• 3𝑥 + 𝑦 < 15

Which one of the following ordered pairs (x,y) is a solution to the inequality
-7x – 5y < -17

• (2, -1)

• (-1, 2)

• (1, 2)

• (2, 1)

Which ordered pair is a solution of the inequality?

y ≥ 4x – 5. Explain how you know you are correct. Be specific.

• (3, 4)

• (3, 0)

• (2, 1)

• (1, 1)

Is the point (2, 6) included in the solution set of the linear inequality?

y < -2x - 5

• Yes, it is included.

• No, it is excluded.