Solving Systems of Linear Inequalities

Question 1

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

Revolt · Accepted Answer

(–2, 2); (0, 0)

Question 2

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.

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

(–4, –2)✔ (–1, –2)X (1, 4)(2, 2)

Revolt · Accepted Answer

✔ (–1, –2)

Question 5

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 6

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

Revolt · Accepted Answer

y > x + 2

Question 7

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 8

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 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?

Revolt · Accepted Answer

y ≤ 2x – 1

Question 10

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.

Solving Systems of Linear Inequalities Answers

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