Q: Which of the following systems would have a solution set that is unbounded?

$$\begin{cases} y \u003e x \\ y \u003e -x \end{cases}$$

Q: A region is shaded above the line $$y = 2x - 3$$ and below the line $$y = -x + 4. $$Which system of inequalities describes this region?

$$\begin{cases} y \u003e 2x - 3 \\ y \u003c -x + 4 \end{cases}$$

Question 1

Which of the following ordered pairs is a solution to the system of inequalities: 
$$\begin{cases} y \u003e 2x + 4 \ y \u003c 2x - 2 \end{cases}$$?

Accepted Answer

There is no solution to this system.

Question 2

What is the first step when graphing the solution set for a system of linear inequalities?

Accepted Answer

Graph each inequality in the system on the same set of axes.

Question 3

Given the system $$\begin{cases} 3x + y \leq 9 \ x - y \u003e 2 \end{cases}$$, which region represents the solution set?

Accepted Answer

The region where the shaded areas of both inequalities overlap.

Question 4

If the boundary line for an inequality is $$y = -x + 3$$ and the inequality is $$y \u003c -x + 3$$, how should the boundary line be drawn?

Accepted Answer

As a dashed line.

Question 5

Which of the following best describes the solution set for the system $$\begin{cases} y \geq 2x - 1 \ y \u003c -x + 4 \end{cases}$$?

Accepted Answer

The region between the two lines where the shaded areas overlap.

Question 6

A company must satisfy the following constraints for production: $$x \geq 0$$, $$y \geq 0$$, $$x + y \leq 10$$, and $$y \leq 2x + 1. $$Which region on the graph represents all possible solutions?

Accepted Answer

The region in the first quadrant below both lines.

Question 7

Which of the following points is a solution to the system $$\begin{cases} y \u003e x - 2 \ y \u003c -2x + 5 \end{cases}$$?

Accepted Answer

$$(1, 2)$$

Question 8

Why is the solution to a system of linear inequalities often a region rather than a single point?

Accepted Answer

Because inequalities represent all points that satisfy the condition, not just those on the line.

Question 9

If a system of inequalities has no overlapping shaded region, what does this mean?

Accepted Answer

There is no solution to the system.

Question 10

A business must keep its advertising budget $$x$$ and production budget $$y$$ within the constraints $$x + y \leq 10000$$ and $$x \geq 2000. $$Which of the following points is a feasible solution?

Accepted Answer

$$(3000, 7000)$$

Question 11

Which of the following systems would have a solution set that is unbounded?

Accepted Answer

$$\begin{cases} y \u003e x \ y \u003e -x \end{cases}$$

Question 12

Given the system $$\begin{cases} y \leq 3x + 2 \ y \geq -x - 1 \end{cases}$$, which of the following points is NOT a solution?

Accepted Answer

$$(1, 4)$$

Question 13

A region is shaded above the line $$y = 2x - 3$$ and below the line $$y = -x + 4. $$Which system of inequalities describes this region?

Accepted Answer

$$\begin{cases} y \u003e 2x - 3 \ y \u003c -x + 4 \end{cases}$$

Question 14

Which of the following best explains why the boundary line for $$y \leq 2x + 1 is $$solid?

Accepted Answer

Because the inequality includes the points on the line.

Question 15

A medical researcher is testing two drugs, $$x$$ and $$y$$, with the constraints $$x \geq 0$$, $$y \geq 0$$, $$x + 2y \leq 100$$, and $$2x + y \leq 120. $$Which point is a possible solution?

Accepted Answer

$$(40, 30)$$

Systems of Linear Inequalities: Graphing and Solution Sets

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