Domanda del libro di testo
In Exercises 47–52, solve each system by the method of your choice.
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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
Capitolo 6, Problema 47
Graph the solution set of each system of inequalities or indicate that the system has no solution.
Guida verificata passo dopo passo1
Identify the first inequality: \(x^{2} + y^{2} \leq 36\). This represents all points inside or on the circle centered at the origin \((0,0)\) with radius \(6\), since \(\sqrt{36} = 6\).
Identify the second inequality: \(3x + y > 6\). This is a linear inequality representing all points above the line \(3x + y = 6\).
Rewrite the linear inequality in slope-intercept form to better understand the boundary line: \(y > -3x + 6\). This line has a slope of \(-3\) and a y-intercept at \((0,6)\).
Graph the circle \(x^{2} + y^{2} = 36\) as a solid boundary because the inequality includes equality (\(\leq\)), meaning points on the circle are included.
Graph the line \(y = -3x + 6\) as a dashed line because the inequality is strict ($>$), meaning points on the line are not included. Then shade the region above this line where \(y > -3x + 6\).
The solution set to the system is the intersection of the shaded region inside the circle and above the line. This means you look for points that satisfy both inequalities simultaneously.
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Graphing Circles and Inequalities
The inequality x² + y² ≤ 36 represents all points inside or on the circle centered at the origin with radius 6. Understanding how to graph this region involves recognizing the circle's boundary (x² + y² = 36) and shading the interior where the inequality holds true.
Video consigliato:
5:18
Circles in Standard Form
Graphing Linear Inequalities
The inequality 3x + y > 6 represents a half-plane above the line 3x + y = 6. To graph it, first plot the boundary line, then determine which side satisfies the inequality by testing a point, shading the region where the inequality is true.
Video consigliato:
06:07Linear Inequalities
Solution Set of a System of Inequalities
The solution set of the system is the intersection of the regions satisfying each inequality. It includes points inside the circle and above the line simultaneously. Identifying this overlap is key to correctly graphing the system and understanding if solutions exist.
Video consigliato:
6:19Systems of Inequalities
Pratica correlata
Domanda del libro di testo
In Exercises 47–48, solve each system by the method of your choice. (x + 2)/2 - (y + 4)/3 = 3 (x + y)/5 = (x - y)/2 - 5/2
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Domanda del libro di testo
In Exercises 47–48, solve each system by the method of your choice. (x - y)/3 = (x + y)/2 - 1/2 (x + 2)/2 - 4 = (y + 4)/3
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Domanda del libro di testo
In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.
This
is a piecewise function. Refer to the textbook.
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Domanda del libro di testo
Graph the solution set of each system of inequalities or indicate that the system has no solution.
560
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Domanda del libro di testo
In Exercises 46–55, graph the solution set of each system of inequalities or indicate that the system has no solution.
This
is a piecewise function. Refer to the textbook.
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