Which of the following shows linear inequality in two variables?

• 6𝑎 - 3𝑎 = 9

• 𝑘 + 4 < 8 + 2𝑘

• 3𝑝 ≤ 4 + 𝑝

• 21𝑚 ≥ 2𝑛 - 15

Answer explanation

The correct choice is 21𝑚 ≥ 2𝑛 - 15, as it represents a linear inequality in two variables (m and n). The other options either represent equations or do not involve two variables in an inequality form.

For what possible values of 𝑥 and 𝑦 will make the inequality 5𝑥 + 3𝑦 > 12 true?

• (0, 3)

• (3, -1)

• (1, -3)

• (3, 0)

Answer explanation

To satisfy 5x + 3y > 12, we test the pairs.
For (3, 0): 5(3) + 3(0) = 15 > 12.
For others: (0, 3) = 9, (3, -1) = 14, (1, -3) = 2, none satisfy the inequality.
Thus, (3, 0) is the only valid solution.

What is the graph of a linear inequality?

• a half plane

• half of parabola

• parabola

• straight line

Answer explanation

The graph of a linear inequality represents all the solutions to the inequality, which forms a half plane.

Which of the following graphs represents the linear inequality x + y > 3?

• 
• 
• 
• 

Kim was asked the inequality symbol to be used to translate at least in the mathematical sentence 8 times a number y minus 3 times a number x is at least 30. Her answer is >. Is she correct?

• Yes, because the symbol for at least is <.

• Yes, because the symbol for at least is >.

• No, because the symbol for at least is ≥.

• No, because the symbol for at least is ≤.

Answer explanation

Kim is incorrect. The phrase 'at least' indicates a minimum value, which is represented by the symbol ≥.

The difference between the scores of Reyner and Lea in Math test is not more than 5 points. If Lea's score is 32 points, what could be the score of Lea?

• 37 and below

• 37 and above

• 27 and above

• 27 and below

Answer explanation

Lea's score is 32. The difference with Reyner's score cannot exceed 5 points, meaning Reyner's score can be between 27 and 37. Therefore, Lea's score must be 37 and below to maintain this difference.

Which ordered pair satisfies the system of linear inequalities in two variables:

• (1, 2)

• (1, 1)

• (2, 2)

• (0, 3)

Answer explanation

The ordered pair (1, 1) satisfies the system of linear inequalities, as it meets all conditions set by the inequalities. The other pairs do not fulfill the requirements, making (1, 1) the correct choice.

The graph at the right shows the graph of a system of linear inequalities in two variables. Which of the following ordered pairs is the solution to this system?

• (4, 2)

• (1, 3)

• (-2, 2)

• (1, -1)

Answer explanation

To determine the solution, we check which ordered pair lies within the shaded region of the graph. The point (1, 3) satisfies all inequalities, while the others do not. Thus, (1, 3) is the correct solution.

Your mother plans to serve pork barbecue and chicken nuggets at your birthday party. She expects to serve at least 50 kilos of meat. Pork costs P200.00 per kilo, and chicken costs P180.00 per kilo. If the allotted budget for meat at your birthday is at most P10,000.00, which of the following are possible quantities of pork and chicken to be bought?

• 10 kilos of pork, 50 kilos of chicken

• 10 kilos of pork, 45 kilos of chicken

• 8 kilos of pork, 45 kilos of chicken

• 8 kilos of pork, 50 kilos of chicken

Answer explanation

To meet the budget and meat requirement, 8 kilos of pork (P1600) and 45 kilos of chicken (P8100) total P9700, satisfying both conditions. Other options exceed the budget or do not meet the 50 kilos minimum.

It is a rule that pairs one unique element of domain to one element of range.

• Domain

• Range

• Function

• Relation

Answer explanation

A function is defined as a relation that pairs each unique element from the domain to exactly one element in the range. This characteristic distinguishes functions from other types of relations.