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Graph: x + y ≤ 18 x + 2y 20 x > 0 y 0

Graph: x + y ≤ 18 x + 2y 20 x > 0 y 0

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Graphing Linear Inequalities In this exercise, you are given a set of inequalities to graph: 1. \( x + y \leq 18 \) 2. \( x + 2y \leq 20 \) 3. \( x \geq 0 \) 4. \( y \geq 0 \) **Hint:** There are 4 inequalities to graph. ### Graph Details The graph is a coordinate grid. The y-axis values range from 21 to 25, labeled sequentially. Use this grid to plot the inequalities and shade the feasible region that satisfies all the inequalities. ### Steps to Graph: 1. **Boundary Lines:** - Draw lines for each inequality. Use solid lines for \(\leq\) or \(\geq\). - For \(x + y = 18\), plot the line where the sum of \(x\) and \(y\) is 18. - For \(x + 2y = 20\), plot the line where \(x\) plus twice \(y\) equals 20. - The lines \(x = 0\) and \(y = 0\) are the x-axis and y-axis respectively. 2. **Shading:** - Determine which side of each line satisfies the inequality. - The region where all shaded areas overlap is the solution set. This graph represents the set of points that satisfy all the inequalities simultaneously.
Transcribed Image Text:### Graphing Linear Inequalities In this exercise, you are given a set of inequalities to graph: 1. \( x + y \leq 18 \) 2. \( x + 2y \leq 20 \) 3. \( x \geq 0 \) 4. \( y \geq 0 \) **Hint:** There are 4 inequalities to graph. ### Graph Details The graph is a coordinate grid. The y-axis values range from 21 to 25, labeled sequentially. Use this grid to plot the inequalities and shade the feasible region that satisfies all the inequalities. ### Steps to Graph: 1. **Boundary Lines:** - Draw lines for each inequality. Use solid lines for \(\leq\) or \(\geq\). - For \(x + y = 18\), plot the line where the sum of \(x\) and \(y\) is 18. - For \(x + 2y = 20\), plot the line where \(x\) plus twice \(y\) equals 20. - The lines \(x = 0\) and \(y = 0\) are the x-axis and y-axis respectively. 2. **Shading:** - Determine which side of each line satisfies the inequality. - The region where all shaded areas overlap is the solution set. This graph represents the set of points that satisfy all the inequalities simultaneously.
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