교과서 질문
In Exercises 19–28, solve each system by the addition method.
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Ch. 5 - Systems of Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
6장, 문제 27
Graph the solution set of each system of inequalities or indicate that the system has no solution.
검증된 단계별 안내1
Step 1: Identify the system of inequalities to graph:
\[\left\{ \begin{array}{l} 2x + 4y \leq 8 \\ 4x + y \leq 4 \end{array} \right.\]
Step 2: Convert each inequality into an equation to find the boundary lines:
For the first inequality: \[2x + 4y = 8\]
For the second inequality: \[4x + y = 4\]
Step 3: Find the intercepts for each boundary line to help graph them:
- For \[2x + 4y = 8\]:
- When \[x=0\], solve for \[y\]: \[4y = 8 \Rightarrow y = 2\]
- When \[y=0\], solve for \[x\]: \[2x = 8 \Rightarrow x = 4\]
- For \[4x + y = 4\]:
- When \[x=0\], solve for \[y\]: \[y = 4\]
- When \[y=0\], solve for \[x\]: \[4x = 4 \Rightarrow x = 1\]
Step 4: Graph the boundary lines using the intercepts found. Since the inequalities are \( \leq \), shade the region below or on each line. To determine which side to shade, pick a test point (usually the origin \(0,0\)) and check if it satisfies the inequality.
Step 5: The solution set to the system is the intersection of the shaded regions from both inequalities. This overlapping region represents all points \((x,y)\) that satisfy both inequalities simultaneously.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
1m주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Graphing Linear Inequalities
Graphing linear inequalities involves plotting the boundary line of the corresponding equation and shading the region that satisfies the inequality. The boundary line is solid if the inequality includes equality (≤ or ≥) and dashed if it does not (< or >). This visual representation helps identify all possible solutions to the inequality.
추천 영상:
06:07
Linear Inequalities
System of Inequalities
A system of inequalities consists of two or more inequalities considered simultaneously. The solution set is the intersection of the regions that satisfy each inequality individually. Graphing both inequalities on the same coordinate plane reveals the common shaded area representing all solutions.
추천 영상:
6:19Systems of Inequalities
Finding Boundary Lines and Test Points
To graph inequalities, first convert each inequality to an equation to find the boundary line. Then, select a test point not on the line (commonly the origin) to determine which side of the line satisfies the inequality. This method ensures accurate shading of the solution region.
추천 영상:
04:27Finding Equations of Lines Given Two Points
관련 실천
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