Solving Systems of Linear Inequalities

Question 1

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

Revolt · Accepted Answer

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

Question 2

(–4, –2)✔ (–1, –2)(1, 4)(2, 2)

Revolt · Accepted Answer

✔ (–1, –2)

Question 3

Which equation represents an inequality in the system of inequalities shown in the graph?

Revolt · Accepted Answer

✔ y < 2x + 2; y < 2x + 2; (–1, –2)

Question 4

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 5

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

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

Question 6

How will the solution of the system y > 2x + and y 2x + ?

Revolt · Accepted Answer

In the original system, the inequality y > 2x + 2/3 shades the region above a line with a y-intercept of 2/3, and y 2x + 2/3. This still results in no common solution because the shaded regions face away from each other and the boundary line is not included.

Question 7

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?

Revolt · Accepted Answer

y ≤ 2x – 1

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

What did you include in your response? Check all that apply.

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 10

What did you include in your response? Check all that apply.

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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