Question 1

Which of the following represents the solution set for the system of inequalities: $$3x - 2y \geq 6$$, $$x + y \leq -2$$, $$y \leq 3$$?

Accepted Answer

The region where all three inequalities overlap, including the boundary lines.

Question 2

What is the equation of the boundary line for the inequality $$3x - 2y \geq 6$$?

Accepted Answer

$$3x - 2y = 6$$

Question 3

If you graph $$y \leq 3$$, which region do you shade?

Accepted Answer

Below the line $$y = 3$$

Question 4

Which point satisfies all three inequalities: $$3x - 2y \geq 6$$, $$x + y \leq -2$$, $$y \leq 3$$?

Accepted Answer

$$( -3, 1 )$$

Question 5

What is the slope of the boundary line $$x + y = -2$$?

Accepted Answer

$$-1$$

Question 6

How would you graph the inequality $$3x - 2y \geq 6$$?

Accepted Answer

Draw the line $$3x - 2y = 6$$ and shade above the line.

Question 7

Which of the following is NOT a step in solving a system of inequalities graphically?

Accepted Answer

Shade only the region above all boundary lines, regardless of the inequality.

Question 8

If the system $$3x - 2y \geq 6$$, $$x + y \leq -2$$, $$y \leq 3$$ represents a feasible region for a business, what does the intersection of all shaded regions represent?

Accepted Answer

The set of all possible solutions that satisfy the business constraints.

Question 9

Which inequality would you use to restrict the solution set to points below $$y = 3$$?

Accepted Answer

$$y \leq 3$$

Question 10

If you want to check whether the point $$(0, 0) is in $$the solution set, which inequality does it fail?

Accepted Answer

$$x + y \leq -2$$

Question 11

What is the y-intercept of the line $$3x - 2y = 6$$?

Accepted Answer

$$y = -3$$

Question 12

Which of the following best describes the solution set for a system of linear inequalities?

Accepted Answer

A region on the coordinate plane where all inequalities are satisfied.

Question 13

If you graph $$x + y \leq -2$$, which region do you shade?

Accepted Answer

Below the line $$x + y = -2$$

Question 14

Which of the following points is NOT in the solution set for the system $$3x - 2y \geq 6$$, $$x + y \leq -2$$, $$y \leq 3$$?

Accepted Answer

$$(2, 4)$$

Question 15

What is the x-intercept of the line $$x + y = -2$$?

Accepted Answer

$$x = -2$$

Graphing the Solution Set of a System of Inequalities

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