Solving Systems of Linear Inequalities

Question 1

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

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

Question 2

y > 2x +2y > –2x – 1y < 2x + 2y < –2x – 1

Revolt · Accepted Answer

y < 2x + 2; (–1, –2)

Question 3

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

Revolt · Accepted Answer

y > 2x + 2 and y < x + 1; (–3, 1)

Question 4

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

Revolt · Accepted Answer

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

Question 5

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

Revolt · Accepted Answer

y > x + 2

Question 6

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

Revolt · Accepted Answer

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

Question 7

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 8

Mr. Hernandez plotted the point (1, 1) on Han’s graph of y ≤ One-half 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?

Revolt · Accepted Answer

y ≤ 2x – 1

Question 9

Sample Response: 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. What did you include in your response? Check all that apply.The point (1, –5) satisfies the first inequalit

Revolt · Accepted Answer

The point (1, –5) satisfies the first inequality but not the second inequality.; The point (1, –5) lies in the shaded area of the first inequality, but not the second inequality.; The point (1, –5) lies on the dashed line of the second inequality, which is not inclusive.; The point (1, –5) is not in the solution set of the system of inequalities.

Solving Systems of Linear Inequalities Answers

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