Systems of 3 Linear and Nonlinear Inequalities

Solve the following system of inequalities graphically: 1) 2x + 3y ≤ 6 2) x - y > 2 3) 3x - 2y < 4

• The solution is the region where none of the graphs overlap.

• The solution is the region where only two of the graphs overlap.

• The solution is the region where only one of the graphs overlap.

• The solution is the region where all three graphs overlap.

Determine whether the point (2, 1) is a solution to the system of inequalities: 1) x + y < 4 2) 2x - y ≥ 1 3) 3x + 2y > 5

• Not sure

• Yes

• No

• Maybe

Solve the following system of inequalities algebraically: 1) 3x - 2y ≤ 5 2) x + 4y > 3 3) 2x - y < 2

• The solution is the region above the line 3x - 2y = 5, below the line x + 4y = 3, and above the line 2x - y = 2.

• The solution is the region below the line 3x - 2y = 5, above the line x + 4y = 3, and below the line 2x - y = 2.

• The solution is the region below the line 3x - 2y = 5, below the line x + 4y = 3, and below the line 2x - y = 2.

• The solution is the region above the line 3x - 2y = 5, above the line x + 4y = 3, and above the line 2x - y = 2.

Graph the solution set for the system of inequalities: 1) x + y > 3 2) 2x - y ≤ 4 3) 3x + 2y < 6

• The solution set for the system of inequalities is the shaded region of the first inequality only.

• The solution set for the system of inequalities is the intersection of the shaded regions from all three inequalities.

• The solution set for the system of inequalities is the union of the shaded regions from all three inequalities.

• The solution set for the system of inequalities is the overlapping region of the shaded regions from all three inequalities.

Determine whether the point (-1, 2) is a solution to the system of inequalities: 1) 2x + y > 3 2) x - 2y < 5 3) 3x + 4y ≥ 2

• No

• Yes

• Maybe

• Not sure

Solve the following system of inequalities algebraically: 1) x + 2y ≤ 4 2) 3x - y > 2 3) 2x + 3y < 6

• The shaded region that satisfies all three inequalities.

• The solution is a rectangle.

• The solution is a line.

• The solution is a single point.

Graph the solution set for the system of inequalities: 1) 2x - y > 3 2) x + 3y ≤ 5 3) 4x + 2y < 8

• The solution set is the region that satisfies only the first inequality.

• The solution set is the shaded region that satisfies all three inequalities.

• The solution set is the region that satisfies only the second inequality.

• The solution set is the region that satisfies only the third inequality.

Determine whether the point (3, -2) is a solution to the system of inequalities: 1) x - y < 2 2) 2x + 3y ≥ 1 3) 4x - 2y > 6

• No

• Maybe

• Yes

• Not sure

Solve the following system of inequalities graphically: 1) 3x + 2y ≤ 5 2) x - 4y > 3 3) 2x + y < 2

• The solution is the region where only one of the graphs overlap.

• The solution is the region where none of the graphs overlap.

• The solution is the region where two of the graphs overlap.

• The solution is the region where all three graphs overlap.

Graph the solution set for the system of inequalities: 1) x + y > 3 2) 2x - y ≤ 4 3) 3x + 2y < 6

• The solution set for the system of inequalities is the union of the shaded regions from all three inequalities.

• The solution set for the system of inequalities is the overlapping region of the shaded regions from all three inequalities.

• The solution set for the system of inequalities is the intersection of the shaded regions from all three inequalities.

• The solution set for the system of inequalities is the shaded region of the first inequality only.