Skip to main content
Ch. 5 - Systems of Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 5 - Systems of Equations and InequalitiesProblem 46
Chapter 6, Problem 46

In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.



This

is a piecewise function. Refer to the textbook.

Verified step by step guidance
1
Step 1: Begin by analyzing the system of inequalities provided in the problem. A system of inequalities typically consists of two or more inequalities that need to be solved simultaneously. If the image is not visible, refer to the textbook for the specific inequalities and their corresponding graphs.
Step 2: Rewrite each inequality in slope-intercept form (y = mx + b) if necessary. This will make it easier to graph each inequality. For example, if an inequality is given as Ax + By ≤ C, solve for y to express it in terms of x.
Step 3: Graph each inequality on the coordinate plane. Use a solid line for inequalities that include equality (≤ or ≥) and a dashed line for strict inequalities (< or >). Shade the region of the graph that satisfies the inequality. For example, if the inequality is y > mx + b, shade above the line.
Step 4: Identify the overlapping shaded regions from all the inequalities in the system. The solution set of the system is the region where all shaded areas intersect. If there is no overlapping region, the system has no solution.
Step 5: Verify the solution by selecting a test point within the overlapping region (if it exists) and substituting it into all inequalities to ensure it satisfies the system. If the test point works for all inequalities, the solution set is correct.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
7m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Systems of Inequalities

A system of inequalities consists of two or more inequalities that share the same variables. The solution set is the region where the graphs of these inequalities overlap. Understanding how to graph each inequality and identify the feasible region is crucial for solving these systems.
Recommended video:
Guided course
6:19
Systems of Inequalities

Graphing Techniques

Graphing techniques involve plotting inequalities on a coordinate plane. This includes determining boundary lines, using dashed or solid lines to indicate whether points on the line are included, and shading the appropriate regions to represent the solution set. Mastery of these techniques is essential for visualizing and solving systems of inequalities.
Recommended video:
Guided course
02:16
Graphs and Coordinates - Example

Piecewise Functions

A piecewise function is defined by different expressions based on the input value. Understanding how to interpret and graph piecewise functions is important, as they can represent complex relationships in systems of inequalities. Recognizing the conditions under which each piece applies helps in accurately graphing the overall function.
Recommended video:
4:56
Function Composition
Related Practice
Textbook Question

In Exercises 39–45, graph each inequality. y ≤ 2^x

1
views
Textbook Question

In Exercises 47–48, solve each system by the method of your choice. (x + 2)/2 - (y + 4)/3 = 3 (x + y)/5 = (x - y)/2 - 5/2

Textbook Question

Graph the solution set of each system of inequalities or indicate that the system has no solution.

{x2+y2≤16x+y>2\(\begin{cases}\)x^2 + y^2 \(\leq\) 16 \(\x\) + y > 2\(\end{cases}\)

4
views
Textbook Question

Graph the solution set of each system of inequalities or indicate that the system has no solution.

{y≥x2−1x−y≥−1\(\begin{cases}\)y \(\geq\) x^2 - 1 \(\x\) - y \(\geq\) -1\(\end{cases}\)

2
views
Textbook Question

Perform each long division and write the partial fraction decomposition of the remainder term. (x4-x2+2)/(x3-x2)

3
views
Textbook Question

In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.


This

is a piecewise function. Refer to the textbook.