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 12
Describe the feasible region for the system: x + y ≤ 5, x ≥ 0, y ≥ 0.
Describe the steps to graph the solution set of a system of two linear inequalities in two variables.
Explain the difference between a system of equations and a system of inequalities.
Explain why the boundary line is included in the solution set for the inequality y ≤ 2x + 5.
Explain why the system x ≥ 0, y ≥ 0, x + y ≤ 10 is often used in linear programming problems.
Given the system: x + 2y ≤ 8, x ≥ 0, y ≥ 0, what is the maximum value of x + y?
Given the system: 3x - 2y ≥ 6 and x + y ≤ 4, is the point (2,1) a solution?
Given the system: x + 2y ≥ 6, x - y ≤ 3, y > 0, find the coordinates of the intersection point of the boundary lines x + 2y = 6 and x - y = 3.
Which of the following best describes the solution to the system: y > x and y < -x? (1) The region above both lines (2) The region below both lines (3) The region between the lines (4) No solution
Which of the following is NOT a possible solution set for a system of two linear inequalities? (1) A region bounded by two lines (2) A single point (3) The entire plane (4) A circle
Which of the following is the solution set for the system: x + y ≥ 4 and x - y ≤ 2? (1) All points above the line x + y = 4 and below the line x - y = 2 (2) All points below the line x + y = 4 and above the line x - y = 2 (3) All points on or above x + y = 4 and on or below x - y = 2 (4) All points on or below x + y = 4 and on or above x - y = 2
Which of the following points is a solution to the system: y ≥ 2x - 1 and y < 3x + 4? (1) (0,0) (2) (1,1) (3) (2,3) (4) (3,10)
Fill in the blank: The boundary line for the inequality y > 2x + 1 is ______ in the graph.
Fill in the blank: The intersection of the solution sets of two inequalities is called the ______ of the system.
Fill in the blank: The solution set of a system of inequalities in two variables is usually a ______ on the coordinate plane.
Fill in the blank: The solution to the system y > x and y < x + 4 is the region ______ the lines y = x and y = x + 4.
Given the system: 3x - 2y ≥ 6 and x + y ≤ 4, is the point (2,1) a solution?
True or False: The solution region for a system of inequalities can be unbounded.
True or False: The solution set of a system of inequalities can be the empty set if the inequalities are inconsistent.
True or False: The solution to a system of inequalities can be a single point.
