Determino Graphicaly the soltön for the System negualeties.. 3x + M12 2x-4-2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Topic Video
Question

please see the attached question.  thanks for your help!

**Determining Graphically the Solution for the System of Inequalities**

Consider the following system of inequalities:

1. \(3x + 4y \geq 12\)
2. \(2x - y \geq -2\)
3. \(0 \leq y \leq 6\)
4. \(x \geq 0\)

To find the solution, follow these steps:

1. **Graph each inequality individually on the coordinate plane:**

   - For the inequality \(3x + 4y \geq 12\):
     - First, convert it into an equation \(3x + 4y = 12\).
     - Graph the line \(3x + 4y = 12\).
     - Since the inequality is \(\geq\), shade the region above the line.

   - For the inequality \(2x - y \geq -2\):
     - Convert it into an equation \(2x - y = -2\).
     - Graph the line \(2x - y = -2\).
     - Since the inequality is \(\geq\), shade the region above the line.

   - For the inequality \(0 \leq y \leq 6\):
     - Graph the horizontal lines \(y = 0\) and \(y = 6\).
     - Shade the region between these two lines.

   - For the inequality \(x \geq 0\):
     - Graph the vertical line \(x = 0\).
     - Shade the region to the right of this line.

2. **Determine the intersection of the shaded regions of all inequalities:**
   - The solution to the system of inequalities is the region where the shaded areas overlap.

3. **Check the boundary conditions:**
   - Points on the boundary lines of each inequality should be tested if necessary to confirm that they satisfy the inequalities.

By graphing these inequalities and finding their intersection, you visually demonstrate the solution set for the given system of inequalities.
Transcribed Image Text:**Determining Graphically the Solution for the System of Inequalities** Consider the following system of inequalities: 1. \(3x + 4y \geq 12\) 2. \(2x - y \geq -2\) 3. \(0 \leq y \leq 6\) 4. \(x \geq 0\) To find the solution, follow these steps: 1. **Graph each inequality individually on the coordinate plane:** - For the inequality \(3x + 4y \geq 12\): - First, convert it into an equation \(3x + 4y = 12\). - Graph the line \(3x + 4y = 12\). - Since the inequality is \(\geq\), shade the region above the line. - For the inequality \(2x - y \geq -2\): - Convert it into an equation \(2x - y = -2\). - Graph the line \(2x - y = -2\). - Since the inequality is \(\geq\), shade the region above the line. - For the inequality \(0 \leq y \leq 6\): - Graph the horizontal lines \(y = 0\) and \(y = 6\). - Shade the region between these two lines. - For the inequality \(x \geq 0\): - Graph the vertical line \(x = 0\). - Shade the region to the right of this line. 2. **Determine the intersection of the shaded regions of all inequalities:** - The solution to the system of inequalities is the region where the shaded areas overlap. 3. **Check the boundary conditions:** - Points on the boundary lines of each inequality should be tested if necessary to confirm that they satisfy the inequalities. By graphing these inequalities and finding their intersection, you visually demonstrate the solution set for the given system of inequalities.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Research Design Formulation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,