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 11
Describe how to test if a point is a solution to a system of inequalities.
Describe the steps to graph the solution set of a system of two linear inequalities in two variables.
Explain the difference between the solution set of a single linear inequality and a system of linear inequalities.
Explain why the system x + y ≥ 2 and x + y ≤ 2 has a solution set that is a line.
Given the system: x + 2y ≤ 8 and x ≥ 0, y ≥ 0, what is the maximum value of y if x is 0?
Given the system: x ≥ 1, y ≤ 3, and x + y ≤ 5, what is the minimum value of x + y?
Given the system: y < x + 2 and y > -x + 1, what is the shape of the solution region?
Given the system: 3x - y > 6 and x + y < 4, is the point (3,0) a solution?
Which of the following best describes the solution set of the system: x ≥ 0, y ≥ 0, x + y ≥ 1?
(1) The first quadrant excluding the origin
(2) The entire first quadrant
(3) The region below the line x + y = 1
(4) The region above the line x + y = 1 in the first quadrant
Which of the following is a solution to the system of inequalities: x + y > 3 and x - y < 1?
(1) (2,2)
(2) (3,1)
(3) (1,3)
(4) (0,0)
Which of the following is NOT a possible solution set for a system of two linear inequalities?
(1) A bounded region
(2) An unbounded region
(3) A single point
(4) A circle
Which of the following points is a solution to the system: y ≤ 2x + 1 and y ≥ x - 2?
(1) (1,0)
(2) (0,2)
(3) (2,5)
(4) (3,1)
A system of inequalities is said to be ________ if there is at least one solution.
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 a system of inequalities in two variables is a ________ on the coordinate plane.
Fill in the blank: The solution set of the system y > 2x and y < 2x is ________.
Given the system: 3x - y > 6 and x + y < 4, is the point (3,0) a solution?
True or False: The point (0,0) is a solution to the system y ≥ 2x and x ≥ 0.
True or False: The solution set of a system of inequalities can be a single point.
True or False: The solution set of a system of inequalities can be empty.
