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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![Graph the solution set of the following system of inequalities:
\[ 4x + 8y \leq 8 \]
\[ 5x + y \leq 10 \]
Use the graphing tool to graph the system of inequalities.
**Graph Description:**
The graph is a coordinate plane ranging from -10 to 10 on both the x and y axes. It is used for plotting the inequalities provided:
1. **Inequality \(4x + 8y \leq 8\):** This inequality can be rewritten as \(y \leq -\frac{1}{2}x + 1\). The line \(y = -\frac{1}{2}x + 1\) would have a slope of \(-\frac{1}{2}\) and a y-intercept at (0, 1). The region below this line represents the solution to this inequality.
2. **Inequality \(5x + y \leq 10\):** This inequality can be rewritten as \(y \leq -5x + 10\). The line \(y = -5x + 10\) would have a slope of -5 and a y-intercept at (0, 10). The region below this line represents the solution to this inequality.
**Solution Set:**
The solution set is the overlapping region that satisfies both inequalities on the graph. This region is typically shaded to indicate where both conditions are met.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd8d9876d-60af-48d4-b446-f0d82bb933f7%2F42711222-d10a-4e5f-9402-685e64cc81d0%2Frm2zhdm_processed.png&w=3840&q=75)
Transcribed Image Text:Graph the solution set of the following system of inequalities:
\[ 4x + 8y \leq 8 \]
\[ 5x + y \leq 10 \]
Use the graphing tool to graph the system of inequalities.
**Graph Description:**
The graph is a coordinate plane ranging from -10 to 10 on both the x and y axes. It is used for plotting the inequalities provided:
1. **Inequality \(4x + 8y \leq 8\):** This inequality can be rewritten as \(y \leq -\frac{1}{2}x + 1\). The line \(y = -\frac{1}{2}x + 1\) would have a slope of \(-\frac{1}{2}\) and a y-intercept at (0, 1). The region below this line represents the solution to this inequality.
2. **Inequality \(5x + y \leq 10\):** This inequality can be rewritten as \(y \leq -5x + 10\). The line \(y = -5x + 10\) would have a slope of -5 and a y-intercept at (0, 10). The region below this line represents the solution to this inequality.
**Solution Set:**
The solution set is the overlapping region that satisfies both inequalities on the graph. This region is typically shaded to indicate where both conditions are met.
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