Question 1

Which of the following best describes the solution set of the system of inequalities $$y \u003e 2x + 1$$ and $$y \u003c -x + 4$$?

Accepted Answer

The region between the two lines.

Question 2

Given the inequality $$2y - 4x \u003c 16$$, which of the following points is in the solution set?

Accepted Answer

$$(0, 0)$$

Question 3

When graphing the inequality $$y \leq 3$$, what type of boundary line should be used?

Accepted Answer

A solid line at $$y = 3$$

Question 4

Which of the following best describes the solution set for $$x \u003e 2$$?

Accepted Answer

All points to the right of $$x = 2$$

Question 5

A company must satisfy the constraints $$5x + 6y \u003c -30$$ and $$2x + 3y \geq -4. $$Which region represents the solution set?

Accepted Answer

The region where both inequalities overlap.

Question 6

If the boundary line for an inequality is $$y = -x + 2$$ and the inequality is $$y \u003e -x + 2$$, which side of the line should be shaded?

Accepted Answer

Above the line

Question 7

Which of the following is the correct first step to graph the inequality $$2y - 4x \u003c 16$$?

Accepted Answer

Rewrite as $$y \u003c 2x + 8$$

Question 8

Which of the following statements about the intersection of two solution sets is correct?

Accepted Answer

It includes only points that satisfy both inequalities.

Question 9

If you are given the system $$y \leq 3$$ and $$x \u003e -1$$, which region should be shaded?

Accepted Answer

Below $$y = 3$$ and to the right of $$x = -1$$

Question 10

Which of the following best describes the union of two solution sets?

Accepted Answer

The set of points that satisfy at least one inequality.

Question 11

A region is defined by $$y \u003c -1. $$Which of the following points is in the solution set?

Accepted Answer

$$(2, -2)$$

Question 12

When graphing $$x \geq 3$$, what type of line and shading should be used?

Accepted Answer

Solid line at $$x = 3$$, shade to the right

Question 13

Which of the following is a correct test point for the inequality $$y \u003c 2x + 5 if $$the boundary line is $$y = 2x + 5$$?

Accepted Answer

$$(0, 0)$$

Question 14

If a solution set is defined by $$y \u003e 2x + 1 or$$ $$y \u003c -x + 4$$, what does the solution set represent?

Accepted Answer

The region outside the area between the two lines.

Question 15

Which of the following is NOT a correct step when solving a linear inequality in two variables?

Accepted Answer

Shade the region that does not satisfy the inequality.

Question 16

If the inequality is $$y \geq 2x - 3$$, which of the following points is NOT in the solution set?

Accepted Answer

$$(1, -5)$$

Question 17

Which of the following best describes the meaning of the symbol $$\cap$$ when joining solution sets?

Accepted Answer

Intersection

Question 18

A region is defined by $$x \leq 2$$ and $$y \u003e -1. $$Which of the following points is in the solution set?

Accepted Answer

$$(2, 0)$$

Question 19

Which of the following is the correct interpretation of the solution set for $$y \leq 3$$?

Accepted Answer

All points below and on the line $$y = 3$$

Question 20

If the solution set is the union of $$A$$ and $$B$$, which of the following is true?

Accepted Answer

It contains all points in $$A or$$ $$B.$$

Systems of Linear Inequalities in Two Variables

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