Systems of Inequalities
Math ⇒ Algebra
Systems of Inequalities starts at 9 and continues till grade 12.
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See sample questions for grade 10
Describe the difference between the solution set of a system of equations and a system of inequalities.
Describe the steps to solve a system of two linear inequalities in two variables.
Explain why the point (0,0) is not a solution to the system: x > 0 and y > 0.
Given the system: 2x + 3y ≤ 12 and x ≥ 0, y ≥ 0, what is the maximum value of x if y = 0?
Explain why the point (0,0) is not a solution to the system: x > 0 and y > 0.
Given the system: x + 2y ≤ 8 and x ≥ 0, y ≥ 0, what is the maximum value of y if x = 0?
Given the system: x + y ≥ 4 and x - y ≤ 2, is the point (3,1) a solution?
Given the system: y > 2x - 1 and y < 4x + 3, find a point that is a solution.
Which of the following best describes the solution set of the system: y > 2x and y < x + 4?
(1) The region above both lines
(2) The region below both lines
(3) The region between the two lines
(4) The region outside both lines
Which of the following is a solution to the system of inequalities: x + y > 3 and x - y < 1?
(1) (2,2)
(2) (1,3)
(3) (0,0)
(4) (3,1)
Which of the following is NOT a step in solving a system of inequalities?
(1) Graph each inequality
(2) Find the intersection region
(3) Shade the region that satisfies only one inequality
(4) Identify boundary lines
Which of the following is the correct method to graph the solution set of a system of inequalities?
(1) Graph each inequality and shade the region that satisfies both
(2) Graph only one inequality
(3) Shade the entire plane
(4) Only plot the intersection points
Fill in the blank: The boundary line for the inequality y ≥ 2x + 1 is _______.
Fill in the blank: The inequality y ≤ 3x - 2 has a boundary line with a _______ slope.
Fill in the blank: The intersection of the solution sets of two inequalities is called the _______ solution set.
Fill in the blank: The solution set of the system x ≥ 2 and y ≤ 3 is the region to the _______ of x = 2 and _______ y = 3.
Given the system: x + y ≥ 4 and x - y ≤ 2, is the point (3,1) a solution?
True or False: The solution set of a system of inequalities can be a line.
True or False: The solution set of a system of inequalities can be a single half-plane.
True or False: The solution set of a system of inequalities can be empty.
