In a Grade 8 math class, students are asked to identify examples of linear inequalities in two variables. The teacher writes several expressions on the board.

Which of the following is NOT a linear inequality in two variables?

• x + y < 5

• y > 2x + 7

• x < 0

• x + y ≥ 12

Mario wants to show to his friend an example of different forms of linear inequality in two variables.

 

Which of the following would NOT be an example of a linear inequality in two variables?

• Ax + By < C

• Ax + By = C

• Ax + By > C

• Ax + By ≤ C

In a game, players earn points based on two activities, Activity X and Activity Y. The total points, represented by the equation x + y > 8, must be greater than 8 for the player to advance to the next level. Each ordered pair (x, y) represents a possible combination of points from Activity X and Activity Y.

 

Which of the following point combinations will satisfy the condition x + y > 8 and allow the player to advance?

• (3, 4)

• (4, 4)

• (5, 6)

• (-10, 1)

The graph of x + y > 5 is presented on the right, examine which ordered pair will satisfy the given linear inequality.

 

• (0, 5)

• (6, 3)

• (1, -2)

• (-5, -1)

A park boundary is mapped using a linear inequality. The shaded area on the map shows all points within the park, and any point in this area is a solution to the inequality.

 

Based on this, how many solutions does a linear inequality in two variables have?

• 0

• 1

• 2

• infinite

In Pasay City, a community organization plans to establish a pedestrian-friendly zone near a busy intersection. They decide that all points within the zone must satisfy the condition where the combined distances from two specific markers, represented by x and y, are less than 4 kilometers. This requirement is represented by the inequality              x + y < 4.

 

Which of the following graphs shows the correct area where x + y < 4?

• 
• 
• 
• 

Write a linear inequality that represents this situation: The amount consisting 50 bills (f) and Php 100 bills (h) is greater than Php 500.

 

• 50f + 100h = 500

• 50f + 100h > 500

• 50f + 100h ≥ 500

• A.    50f + 100h < 500

Maria is making bags and wallets from recycled materials. It takes 5 hours to make a bag (x) and 2 hours to make a wallet (y). If she can work no more than 34 hours a week, and she makes 4 bags, what is the maximum number of wallets she can make in the remaining time?

• 5

• 6

• 7

• 8

Determine the solution of the system of linear inequality,

• (2, 4)

• (6, -2)

• (0, 2)

• (3, 0)

In Manila, two environmental zones are defined on a map, represented by a system of linear inequalities that restricts certain types of construction. The shaded region on the graph represents the area where both inequalities overlap, indicating the safe zone for green infrastructure projects.

 

Given the graph at the right, which point is a solution that satisfies both inequalities in this system?

• (2, 3)

• (1, 6)

• (-3, 4)

• (3, -2)