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7th Edition

James Stewart + 2 others

Publisher: Brooks Cole

ISBN: 9781305071759

Chapter 10.9, Problem 41E

Textbook Problem

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**Systems of Inequalities** Graph the solution set of the system of inequalities. Find the coordinates of all vertices, and determine whether the solution set is bounded.

**41.**

To determine

**To evaluate:** The graph of the given set of inequalities with coordinates of all vertices and check whether the solution is bounded or not.

**Section1:**

The given inequalities are,

Inequality (1) represents the region towards the origin that is below the line

The inequality (2) represents the region towards the origin and left side of the line

From above given information, sketch the graph of inequalities,

Figure (1)

From the above Figure (1), the intersection points are

Thus, the solution of the system is common region of inequalities.

Figure (2)

The solution set of inequalities is shown in shaded region of above Figure (2).

**Section2:**

The equations of the lines are,

For equations (1) and (2),

Substitute
*y* from equation (2) in equation (1), the equation (1) becomes,

Solve the above quadratic equation

Precalculus: Mathematics for Calculus (Standalone Book)

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Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fraction Decomposition Find the partial...Ch. 10.7 - Partial Fractions Determine A and B in terms of a...Ch. 10.7 - Partial Fractions Determine A, B, C, and D in...Ch. 10.7 - DISCUSS: Recognizing Partial Fraction...Ch. 10.7 - DISCUSS: Assembling and Disassembling Partial...Ch. 10.8 - The system of equations {2yx2=0yx=4 is graphed...Ch. 10.8 - The system of equations {2yx2=0yx=4 is graphed...Ch. 10.8 - Substitution Method Use the substitution method to...Ch. 10.8 - Substitution Method Use the substitution method to...Ch. 10.8 - Substitution Method Use the substitution method to...Ch. 10.8 - Substitution Method Use the substitution method to...Ch. 10.8 - Substitution Method Use the substitution method to...Ch. 10.8 - Substitution Method Use the substitution method to...Ch. 10.8 - Elimination Method Use the elimination method to...Ch. 10.8 - Elimination Method Use the elimination method to...Ch. 10.8 - Elimination Method Use the elimination method to...Ch. 10.8 - Elimination Method Use the elimination method to...Ch. 10.8 - Elimination Method Use the elimination method to...Ch. 10.8 - Elimination Method Use the elimination method to...Ch. 10.8 - Finding Intersection Points Graphically Two...Ch. 10.8 - Finding Intersection Points Graphically Two...Ch. 10.8 - Finding Intersection Points Graphically Two...Ch. 10.8 - Finding Intersection Points Graphically Two...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Solving Nonlinear Systems Find all solutions of...Ch. 10.8 - Graphical Method Use the graphical method to find...Ch. 10.8 - Graphical Method Use the graphical method to find...Ch. 10.8 - Graphical Method Use the graphical method to find...Ch. 10.8 - Graphical Method Use the graphical method to find...Ch. 10.8 - Graphical Method Use the graphical method to find...Ch. 10.8 - Graphical Method Use the graphical method to find...Ch. 10.8 - Graphical Method Use the graphical method to find...Ch. 10.8 - Graphical Method Use the graphical method to find...Ch. 10.8 - Some Trickier Systems Follow the hints and solve...Ch. 10.8 - Some Trickier Systems Follow the hints and solve...Ch. 10.8 - Some Trickier Systems Follow the hints and solve...Ch. 10.8 - Some Trickier Systems Follow the hints and solve...Ch. 10.8 - Legs of a Right Triangle A right triangle has an...Ch. 10.8 - Dimensions of a Rectangle A rectangle has an area...Ch. 10.8 - Dimensions of a Rectangle The perimeter of a...Ch. 10.8 - Dimensions of a Rectangle A circular piece of...Ch. 10.8 - Flight of a Rocket A hill is inclined so that its...Ch. 10.8 - Making a Stovepipe A rectangular piece of sheet...Ch. 10.8 - Global Positioning System (GPS) The Global...Ch. 10.8 - DISCOVER PROVE: Intersection of a Parabola and a...Ch. 10.9 - If the point (2, 3) is a solution of an inequality...Ch. 10.9 - To graph an inequality, we first graph the...Ch. 10.9 - If the point (2, 3) is a solution of a system of...Ch. 10.9 - Shade the solution of each system of inequalities...Ch. 10.9 - Solutions of Inequalities An inequality and...Ch. 10.9 - Solutions of Inequalities An inequality and...Ch. 10.9 - Solutions of Systems of Inequalities A system of...Ch. 10.9 - Solutions of Systems of Inequalities A system of...Ch. 10.9 - Graphing Inequalities 9. y 2xCh. 10.9 - Graphing Inequalities 10. y 3xCh. 10.9 - Graphing Inequalities 11. y 2Ch. 10.9 - Graphing Inequalities 12. x 1Ch. 10.9 - Graphing Inequalities 13. x 2Ch. 10.9 - Graphing Inequalities 14. y 1Ch. 10.9 - Graphing Inequalities 15. y x 3Ch. 10.9 - Graphing Inequalities 16. y 1 xCh. 10.9 - Graphing Inequalities 17. 2x y 4Ch. 10.9 - Graphing Inequalities 18. 3x y 9 0Ch. 10.9 - Graphing Inequalities 19. x2 + y 5Ch. 10.9 - Graphing Inequalities 20. y x2 +1Ch. 10.9 - Graphing Inequalities 21. x2 + y2 9Ch. 10.9 - Graphing Inequalities 22. x2 + (y 2)2 4Ch. 10.9 - Graphing Inequalities Use a graphing calculator to...Ch. 10.9 - Graphing Inequalities Use a graphing calculator to...Ch. 10.9 - Graphing Inequalities Use a graphing calculator to...Ch. 10.9 - Graphing Inequalities Use a graphing calculator to...Ch. 10.9 - Finding Inequalities from a Graph An equation and...Ch. 10.9 - Finding Inequalities from a Graph An equation and...Ch. 10.9 - Finding Inequalities from a Graph An equation and...Ch. 10.9 - Finding Inequalities from a Graph An equation and...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the solution set of...Ch. 10.9 - Systems of Inequalities Graph the system of...Ch. 10.9 - Systems of Inequalities Graph the system of...Ch. 10.9 - Systems of Inequalities Graph the system of...Ch. 10.9 - Systems of Inequalities Graph the system of...Ch. 10.9 - Systems of Inequalities Graph the system of...Ch. 10.9 - Systems of Inequalities Graph the system of...Ch. 10.9 - Graphing Systems of Inequalities Use a graphing...Ch. 10.9 - Graphing Systems of Inequalities Use a graphing...Ch. 10.9 - Graphing Systems of Inequalities Use a graphing...Ch. 10.9 - Graphing Systems of Inequalities Use a graphing...Ch. 10.9 - Planting Crops A farmer has 500 acres of arable...Ch. 10.9 - Planting Crops A farmer has 300 acres of arable...Ch. 10.9 - Publishing Books A publishing company publishes a...Ch. 10.9 - Furniture Manufacturing A man and his daughter...Ch. 10.9 - Coffee Blends A coffee merchant sells two...Ch. 10.9 - Nutrition A cat food manufacturer uses fish and...Ch. 10.9 - DISCUSS: Shading Unwanted Regions To graph the...Ch. 10 - (a) What are the three methods we use to solve a...Ch. 10 - For a system of two linear equations in two...Ch. 10 - What operations can be performed on a linear...Ch. 10 - (a) Explain how Gaussian elimination works. (b)...Ch. 10 - What does it mean to say that A is a matrix with...Ch. 10 - What is the row-echelon form of a matrix? What is...Ch. 10 - (a) What is the augmented matrix of a system? What...Ch. 10 - Suppose you have used Gaussian elimination to...Ch. 10 - What is the reduced row echelon form of a matrix?Ch. 10 - (a) How do Gaussian elimination and Gauss-Jordan...Ch. 10 - If A and B are matrices with the same dimension...Ch. 10 - (a) What must be true of the dimensions of A and B...Ch. 10 - (a) What is an identity matrix In? If A is an n n...Ch. 10 - (a) Express the system in 1(b) as a matrix...Ch. 10 - (a) Is it true that the determinant det A of a...Ch. 10 - (a) How do we express a rational function r as a...Ch. 10 - (a) How do we graph an inequality in two...Ch. 10 - Systems of Linear Equations in Two Variables Solve...Ch. 10 - Systems of Linear Equations in Two Variables Solve...Ch. 10 - Systems of Linear Equations in Two Variables Solve...Ch. 10 - Systems of Linear Equations in Two Variables Solve...Ch. 10 - Systems of Linear Equations in Two Variables Solve...Ch. 10 - Systems of Linear Equations in Two Variables Solve...Ch. 10 - Systems of Nonlinear Equations Solve the system of...Ch. 10 - Systems of Nonlinear Equations Solve the system of...Ch. 10 - Systems of Nonlinear Equations Solve the system of...Ch. 10 - Systems of Nonlinear Equations Solve the system of...Ch. 10 - Systems of Nonlinear Equations Use a graphing...Ch. 10 - Systems of Nonlinear Equations Use a graphing...Ch. 10 - Systems of Nonlinear Equations Use a graphing...Ch. 10 - Systems of Nonlinear Equations Use a graphing...Ch. 10 - Matrices A matrix is given. (a) State the...Ch. 10 - Matrices A matrix is given. (a) State the...Ch. 10 - Matrices A matrix is given. (a) State the...Ch. 10 - Matrices A matrix is given. (a) State the...Ch. 10 - Matrices A matrix is given. (a) State the...Ch. 10 - Matrices A matrix is given. (a) State the...Ch. 10 - {x+y+2z=62x+5z=12x+2y+3z=9Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - {x3y+z=44xy+15z=5Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Systems of Linear Equations in Several Variables...Ch. 10 - Investments A man invests his savings in two...Ch. 10 - Number of Coins A piggy bank contains 50 coins,...Ch. 10 - Investments Clarisse invests 60,000 in...Ch. 10 - Number of Fish Caught A commercial fisherman...Ch. 10 - Matrix Operations Let...Ch. 10 - Matrix Operations Let...Ch. 10 - Matrix Operations Let...Ch. 10 - Matrix Operations Let...Ch. 10 - Matrix Operations Let...Ch. 10 - Matrix Operations Let...Ch. 10 - Matrix Operations Let...Ch. 10 - Matrix Operations Let...Ch. 10 - Matrix Operations Let...Ch. 10 - Matrix Operations Let...Ch. 10 - Matrix Operations Let...Ch. 10 - Matrix Operations Let...Ch. 10 - Inverse Matrices Verify that the matrices A and B...Ch. 10 - Inverse Matrices Verify that the matrices A and B...Ch. 10 - Matrix Equations Solve the matrix equation for the...Ch. 10 - Matrix Equations Solve the matrix equation for the...Ch. 10 - Matrix Equations Solve the matrix equation for the...Ch. 10 - Matrix Equations Solve the matrix equation for the...Ch. 10 - Matrix Equations Solve the matrix equation for the...Ch. 10 - Matrix Equations Solve the matrix equation for the...Ch. 10 - Determinants and Inverse Matrices Find the...Ch. 10 - Determinants and Inverse Matrices Find the...Ch. 10 - Determinants and Inverse Matrices Find the...Ch. 10 - Determinants and Inverse Matrices Find the...Ch. 10 - Determinants and Inverse Matrices Find the...Ch. 10 - Determinants and Inverse Matrices Find the...Ch. 10 - Determinants and Inverse Matrices Find the...Ch. 10 - Determinants and Inverse Matrices Find the...Ch. 10 - Using Inverse Matrices to solve a System Express...Ch. 10 - Using Inverse Matrices to solve a System Express...Ch. 10 - Using Inverse Matrices to solve a System Express...Ch. 10 - Using Inverse Matrices to solve a System Express...Ch. 10 - Using Cramers Rule to Solve a System Solve the...Ch. 10 - Using Cramers Rule to Solve a System Solve the...Ch. 10 - Using Cramers Rule to Solve a System Solve the...Ch. 10 - Using Cramers Rule to Solve a System Solve the...Ch. 10 - Area of a Triangle Use the determinant formula for...Ch. 10 - Area of a Triangle Use the determinant formula for...Ch. 10 - Partial Fraction Decomposition Find the partial...Ch. 10 - Partial Fraction Decomposition Find the partial...Ch. 10 - Partial Fraction Decomposition Find the partial...Ch. 10 - Partial Fraction Decomposition Find the partial...Ch. 10 - Partial Fraction Decomposition Find the partial...Ch. 10 - Partial Fraction Decomposition Find the partial...Ch. 10 - Intersection Points Two equations and their graphs...Ch. 10 - Intersection Points Two equations and their graphs...Ch. 10 - Intersection Points Two equations and their graphs...Ch. 10 - Intersection Points Two equations and their graphs...Ch. 10 - Finding an Inequality from a Graph An equation and...Ch. 10 - Finding an Inequality from a Graph An equation and...Ch. 10 - Graphing Inequalities Graph the inequality. 97. 3x...Ch. 10 - Graphing Inequalities Graph the inequality. 98. y ...Ch. 10 - Graphing Inequalities Graph the inequality. 99. x2...Ch. 10 - Graphing Inequalities Graph the inequality. 100. x...Ch. 10 - Solution Set of a System of Inequalities The...Ch. 10 - Solution Set of a System of Inequalities The...Ch. 10 - Solution Set of a System of Inequalities The...Ch. 10 - Solution Set of a System of Inequalities The...Ch. 10 - Systems of Inequalities Graph the solution set of...Ch. 10 - Systems of Inequalities Graph the solution set of...Ch. 10 - Systems of Inequalities Graph the solution set of...Ch. 10 - Systems of Inequalities Graph the solution set of...Ch. 10 - General Systems of Equations Solve for x, y, and z...Ch. 10 - General Systems of Equations Solve for x, y, and z...Ch. 10 - General Systems of Equations For what values of k...Ch. 10 - General Systems of Equations For what value of k...Ch. 10 - A system of equation is given. (a) Determine...Ch. 10 - A system of equation is given. (a) Determine...Ch. 10 - Use a graphing device to find all solutions of the...Ch. 10 - In 212h an airplane travels 600 km against the...Ch. 10 - Determine whether each matrix is in reduced...Ch. 10 - Use Gaussian elimination to find the complete...Ch. 10 - Use Gauss-Jordan elimination to find the complete...Ch. 10 - Anne, Barry, and Cathy enter a coffee shop. Anne...Ch. 10 - Let A=[2324]B=[241130]C=[104112013] Carry out the...Ch. 10 - (a) Write a matrix equation equivalent to the...Ch. 10 - Only one of the following matrices has an inverse....Ch. 10 - Solve using Cramers Rule:...Ch. 10 - Find the partial fraction decomposition of the...Ch. 10 - Graph the solution set of the system of...Ch. 10 - Find the maximum and minimum values of the given...Ch. 10 - Find the maximum and minimum values of the given...Ch. 10 - Find the maximum and minimum value of the given...Ch. 10 - Find the maximum and minimum value of the given...Ch. 10 - Making Furniture A furniture manufacturer makes...Ch. 10 - A Housing Development A housing contractor has...Ch. 10 - Hauling Fruit A trucker hauls citrus fruit from...Ch. 10 - Manufacturing Calculators A manufacturer of...Ch. 10 - Shipping Televisions An electronics discount chain...Ch. 10 - Delivering Plywood A man owns two building supply...Ch. 10 - Packaging Nuts A confectioner sells two types of...Ch. 10 - Feeding Lab Rabbits A biologist wishes to feed...Ch. 10 - Investing in Bonds A woman wishes to invest 12,000...Ch. 10 - Annual Interest Yield Refer to Problem 13. Suppose...Ch. 10 - Business Strategy A small software company...Ch. 10 - Feasible Region All parts of this problem refer to...

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