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 9
Describe the steps to graph the solution set of a system of two linear inequalities.
Explain how to test if a point is a solution to a system of inequalities.
Explain why the point (0,0) is not a solution to the system: y > 2x + 1 and x > 0.
Explain why the solution set of a system of inequalities is often shown as a shaded region on a graph.
Explain why the point (0,0) is not a solution to the system: y > 2x + 1 and x > 0.
Given the system: x + y > 3 and x - y < 1, find a point that is a solution.
Given the system: y < 2x + 3 and y > -x - 1, is the point (2,4) a solution?
Given the system: y > 2x - 1 and y < 2x + 3, what is the range of possible y-values for x = 1?
Which of the following best describes the boundary line for the inequality y > x - 4? (1) Solid and included (2) Dashed and not included (3) Solid and not included (4) Dashed and included
Which of the following best describes the solution set of a system of two linear inequalities in two variables? (1) A line (2) A region in the plane (3) A single point (4) No solution
Which of the following is a possible solution to the system: x > 1, y < 2, and x + y < 5? (1) (2,1) (2) (3,3) (3) (1,1) (4) (2,3)
Which of the following is a system of inequalities? (1) y > 2x + 1 and y < 3x - 4 (2) y = 2x + 1 and y = 3x - 4 (3) y > 2x + 1 and y = 3x - 4 (4) y < 2x + 1 only
Fill in the blank: If two inequalities have no overlapping solution, their system is said to be ________.
Fill in the blank: The boundary line for the inequality y ≤ 3x + 2 is drawn as a ________ line.
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 x > 2 and x < 5 is the interval ________.
Given the system: y < 2x + 3 and y > -x - 1, is the point (2,4) a solution?
Given the system: y ≥ -x + 2 and y < 3x - 1, is the point (1,2) a solution?
True or False: The solution region of a system of inequalities can be a line segment.
True or False: The solution set of a system of inequalities can be empty.
