Solving Systems of Linear Inequalities

Question 1

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

Revolt · Accepted Answer

(1,1); (2, 2)

Question 2

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 3

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

Revolt · Accepted Answer

y > x + 2

Question 4

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 5

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 6

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 7

(–4, –2)✔ (–1, –2)(1, 4)(2, 2)

Revolt · Accepted Answer

✔ (–1, –2)

Question 8

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 9

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

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 10

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

Solving Systems of Linear Inequalities Answers

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