Solving Systems of Linear Inequalities

Question 1

Which ordered pairs make both inequalities true? Check all that apply.(–2, 2)(0, 0)(1,1)(1, 3)(2, 2)

Revolt · Accepted Answer

A: (–2, 2); B: (0, 0)

Question 2

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

Revolt · Accepted Answer

A: y > 2x – 2 and y < x – 1; (3, 1)

Question 3

Which statements are true about the graph of y ≤ 3x + 1 and y ≥ –x + 2? Check all that apply.The slope of one boundary line is 2.Both boundary lines are solid.A solution to the system is (1, 3).Both inequalities are shaded below the boundary lines.The boundary lines intersect.

Revolt · Accepted Answer

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Question 4

Question 4

Revolt · Accepted Answer

The system of linear inequalities has no solution. Both equations have the same slope of -1, which means the boundary lines are parallel. Since the first inequality describes the region above the line $y = -x + 3$ and the second inequality describes the region below the line $y = -x - 2$, the shaded regions move in opposite directions and do not overlap. Because there are no points in common, the system has no solution.

Question 5

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

Revolt · Accepted Answer

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

Question 6

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

Revolt · Accepted Answer

C: y > x + 2

Question 7

Which is the graph of the system x + 3y > –3 and y < x + 1?

Revolt · Accepted Answer

D: [Image: On a coordinate plane, 2 dashed lines are shown. T...]

Question 8

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

Revolt · Accepted Answer

Algebraically, substituting (1, -5) into the inequalities yields -5 ≤ 3(1) + 2, which simplifies to -5 ≤ 5 (true), and -5 > -2(1) - 3, which simplifies to -5 > -5 (false). Graphically, the point (1, -5) lies within the shaded region of the first inequality's solid line but lies directly on the dashed boundary line of the second inequality. Because points on a dashed line are excluding, and the second inequality is not satisfied, (1, -5) is not a solution to the system.

Question 9

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

Revolt · Accepted Answer

D: y ≤ 2x – 1

Question 10

Sample Response: 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.

Revolt · Accepted Answer

A: The shaded area would reverse on both inequalities.; B: The graphs do not overlap until the signs are reversed.; C: There are an infinite number of solutions in the system once the signs are reversed.; D: There are no solutions before they are reversed.

Solving Systems of Linear Inequalities Answers

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