Worksheet Chapter 6: Linear Inequalities in Two Variables

1. Write a linear inequality for each of the following real-world situations:
(a) A delivery truck carries x small packages and y large packages. The maximum payload count is 120 packages.
(b) The price of a shirt is RM x and a pair of trousers is RM y. Encik Ahmad spends at least RM 250 buying 3 shirts and 2 pairs of trousers.

2. True or False: The point (3, 2) is part of the solution region for the inequality 2x - y > 4.

3. Given the boundary line equation 2y = -3x + 12:
(a) Find the x-intercept and y-intercept of the boundary line.
(b) State the linear inequality if the shaded region lies strictly above this boundary line.

4. A factory produces two types of chairs, standard (x) and deluxe (y). The production is subject to the following constraints:
- Machine process time: Each standard chair takes 1 hour and each deluxe chair takes 2 hours. Total available machine time is 40 hours per week.
- Assembly time: Each standard chair takes 2 hours and each deluxe chair takes 1 hour. Total available assembly time is 50 hours per week.
- Non-zero constraint: Production counts cannot be negative.
(a) Write a system of linear inequalities for the constraints.
(b) Determine whether producing 15 standard chairs and 10 deluxe chairs per week satisfies all constraints.

5. A school sports day committee sells T-shirts (x) and caps (y) to raise funds. The conditions for the sale are as follows:
I. The total number of items sold is at least 50.
II. The number of T-shirts sold is at most twice the number of caps sold.
III. The maximum budget allocated is RM 600, where a T-shirt costs RM 12 and a cap costs RM 6.
Write down the system of three linear inequalities representing all the conditions above.

6. Determine whether the point (-1, 4) satisfies the linear inequality 3x + 2y ≥ 5. Show your calculations.

7. Fill in the blank: In graphing linear inequalities, a ________ line is used when the inequality symbol contains '<' or '>'.

8. True or False: The inequality 5x - y² ≤ 10 is a linear inequality in two variables.

9. State the three linear inequalities that define the shaded triangular region bounded by the y-axis (x = 0), the horizontal line y = 2, and the line x + y = 6 in the first quadrant.

10. Which of the following phrases represents the inequality symbol '≥'?