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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![**Problem 4: Graph the Solution for the System of Inequalities**
We are given a system of inequalities to graph:
\[
\begin{align*}
1. \quad & x + y > 5 \\
2. \quad & 2x - y < 4 \\
\end{align*}
\]
**Instructions for Graphing:**
1. **Inequality 1: \(x + y > 5\)**
- Begin by converting the inequality into an equation: \(x + y = 5\).
- Graph the line \(x + y = 5\). This line will be a boundary for the inequality.
- Since the inequality is \(>\), we will shade above the line. Use a dashed line for the boundary because the inequality does not include the line itself.
2. **Inequality 2: \(2x - y < 4\)**
- Convert the inequality into an equation: \(2x - y = 4\).
- Graph the line \(2x - y = 4\). It serves as a boundary.
- Since the inequality is \(<\), shade below the line. Use a dashed line again to indicate the boundary is not included.
**Combining the Solutions:**
- The solution set for this system is the region where the shaded areas overlap. Check the intersecting region to ensure both conditions are satisfied.
By graphing both inequalities and identifying the overlapping shaded region, we determine the solution set, which provides all the \((x, y)\) pairs that satisfy both inequalities simultaneously.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1e2c457e-7496-46a0-a4cb-00bc8d225b21%2F10381e25-75c7-46fa-a272-d5b451726150%2Fgrkpm7d_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 4: Graph the Solution for the System of Inequalities**
We are given a system of inequalities to graph:
\[
\begin{align*}
1. \quad & x + y > 5 \\
2. \quad & 2x - y < 4 \\
\end{align*}
\]
**Instructions for Graphing:**
1. **Inequality 1: \(x + y > 5\)**
- Begin by converting the inequality into an equation: \(x + y = 5\).
- Graph the line \(x + y = 5\). This line will be a boundary for the inequality.
- Since the inequality is \(>\), we will shade above the line. Use a dashed line for the boundary because the inequality does not include the line itself.
2. **Inequality 2: \(2x - y < 4\)**
- Convert the inequality into an equation: \(2x - y = 4\).
- Graph the line \(2x - y = 4\). It serves as a boundary.
- Since the inequality is \(<\), shade below the line. Use a dashed line again to indicate the boundary is not included.
**Combining the Solutions:**
- The solution set for this system is the region where the shaded areas overlap. Check the intersecting region to ensure both conditions are satisfied.
By graphing both inequalities and identifying the overlapping shaded region, we determine the solution set, which provides all the \((x, y)\) pairs that satisfy both inequalities simultaneously.
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