10 questions · Form 4 Mathematics Bab 6: Linear Inequalities in Two Variables
Identify the point that satisfies the system of inequalities: y ≤ x + 2 and y > -2x.
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. Identify the point that satisfies the system of inequalities: y ≤ x + 2 and y > -2x.
Answer: B
Test point (1, 1): 1 ≤ 1 + 2 = 3 (True) and 1 > -2(1) = -2 (True). Both inequalities are satisfied.
2. Which point satisfies the inequality 2x + y < 5?
Answer: B
Substitute coordinates into 2x + y: For (1, 2): 2(1) + 2 = 4 < 5 (True). For (2, 1): 2(2) + 1 = 5, which is not strictly less than 5.
3. Consider the system: y > x, y < 4, x > 0. Which of the following points lies inside this feasible region?
Answer: A
Testing point (1, 3): 3 > 1 (True), 3 < 4 (True), 1 > 0 (True). All three conditions hold.
4. What type of line is drawn on a graph to represent the inequality y ≥ 2x + 1?
Answer: B
Inequalities containing '≥' or '≤' include the points on the boundary line, so they are drawn with a solid line.
5. Does the origin (0, 0) satisfy the inequality 3x - 4y ≥ -12?
Answer: A
Substitute (0, 0): 3(0) - 4(0) = 0. Since 0 ≥ -12 is True, the origin satisfies the inequality.
6. Which of the following points lies in the solution set of y > 3x - 2?
Answer: C
Substitute (0, 0): 0 > 3(0) - 2 ⇒ 0 > -2, which is a true statement.
7. Which inequality corresponds to the region to the right of the vertical line x = 3, excluding the line itself?
Answer: B
Regions to the right of a vertical line correspond to greater values of x. Excluding the line requires the strictly greater symbol '>'.
8. Given the system x ≥ 0, y ≥ 0, x + y ≤ 6. What shape is formed by the solution region in the first quadrant?
Answer: B
The lines x = 0 (y-axis), y = 0 (x-axis), and x + y = 6 enclose a right-angled triangular region in the first quadrant.
9. If a point lies directly on a dashed boundary line of a shaded region, is it a solution to the inequality?
Answer: B
Points on a dashed line are excluded from the solution set because the inequality symbol is strict (< or >).
10. Which of the following is NOT a linear inequality in two variables?
Answer: C
Option C contains y², which makes it a non-linear inequality.