Solving Systems of Linear Inequalities: Assignment

Which ordered pairs make both inequalities true? Check all that apply.

3. (1, 1) 5. (2, 2)

Graphically, a point is a solution to a system of two inequalities if and only if the point

C. lies in the shaded regions of both the top and bottom inequalities.

Which linear inequality will not have a shared solution set with the graphed linear inequality?

C. y > 5/3x + 2

How will the solution of the system y > 2x + 2/3 and y < 2x + 1/3 change if the inequality sign on both inequalities is reversed to y < 2x + 2/3 and y > 2x + 1/3?

Sample Answer: There is no solution to the system in its original form. There are no points in common. If the signs are reversed, the system has an intersection with an infinite number of solutions.

Which statements are true about the graph of y ≤ 3x + 1 and y ≥ -x + 2? Check all that apply.

2. Both boundary lines are solid. 3. A solution to the system is (1, 3). 5. The boundary lines intersect.

Which equation represents an inequality in the system of inequalities shown in the graph? Which point is a solution to the system?

1. y<2x+2 2. (-1, -2)

Which is the graph of the system x + 3y > -3 and y < 1/2x + 1?

D. Graph 4

Determine the relationship between the point (1, -5) and the given system of inequalities. y ≤ 3x + 2 y > -2x - 3 Explain your answer both algebraically and graphically.

Sample Answer: Algebraically, the point (1, -5) satisfies the first inequality, but it does not satisfy the second inequality because -5 is not greater than -5. Graphically, the point (1, -5) lies in the shaded area of the first inequality but lies on the dashed line of the second inequality, which is not inclusive. Therefore (1, -5) is not a solution to the given system of inequalities.

Which system of inequalities with a solution point is represented by the graph?

D. y > 2x + 2 and y < -1/2x + 1; (-3, 1)

Mr. Hernandez plotted the point (1, 1) on Han's graph of y ≤ 1/2x + 2. He instructed Han to add a second inequality to the graph that would include the solution (1, 1). Which equation could Miguel write?

D. y ≤ 2x - 1