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х — 2у < 4 12х + Зу 2 6 - Graph the system of linear inequalities:

х — 2у < 4 12х + Зу 2 6 - Graph the system of linear inequalities:

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Title: Graphing Systems of Linear Inequalities --- **Objective**: Learn how to graph the following system of linear inequalities. **System of Inequalities**: 1. \( x - 2y \leq 4 \) 2. \( 2x + 3y \geq 6 \) **Instructions**: 1. **Graph each inequality separately**: - For \( x - 2y \leq 4 \): - Rearrange to slope-intercept form: \( y \geq \frac{1}{2}x - 2 \). - Graph the line \( y = \frac{1}{2}x - 2 \) using a dashed line (since the inequality is inclusive). - Shade the region below the line. - For \( 2x + 3y \geq 6 \): - Rearrange to slope-intercept form: \( y \geq -\frac{2}{3}x + 2 \). - Graph the line \( y = -\frac{2}{3}x + 2 \) using a solid line (since the inequality is inclusive). - Shade the region above the line. 2. **Solution Region**: - The solution to the system is the region where the shaded areas overlap. - Highlight this region to distinguish it from the non-solution areas. **Practice Exercise**: - Try graphing another set of inequalities and identify the solution region to reinforce your understanding.
Transcribed Image Text:Title: Graphing Systems of Linear Inequalities --- **Objective**: Learn how to graph the following system of linear inequalities. **System of Inequalities**: 1. \( x - 2y \leq 4 \) 2. \( 2x + 3y \geq 6 \) **Instructions**: 1. **Graph each inequality separately**: - For \( x - 2y \leq 4 \): - Rearrange to slope-intercept form: \( y \geq \frac{1}{2}x - 2 \). - Graph the line \( y = \frac{1}{2}x - 2 \) using a dashed line (since the inequality is inclusive). - Shade the region below the line. - For \( 2x + 3y \geq 6 \): - Rearrange to slope-intercept form: \( y \geq -\frac{2}{3}x + 2 \). - Graph the line \( y = -\frac{2}{3}x + 2 \) using a solid line (since the inequality is inclusive). - Shade the region above the line. 2. **Solution Region**: - The solution to the system is the region where the shaded areas overlap. - Highlight this region to distinguish it from the non-solution areas. **Practice Exercise**: - Try graphing another set of inequalities and identify the solution region to reinforce your understanding.
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