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7th Edition

James Stewart + 2 others

Publisher: Brooks Cole

ISBN: 9781305071759

Chapter 10.1, Problem 12E

Textbook Problem

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**Elimination Method** Use the elimination method to find all solutions of the system of equations.

**12.**

To determine

**To find:** The solution of given equations using elimination method.

**Given:**

The given equations are,

**Calculation:**

Multiply equation (1) by 3 to make the coefficients of *x*-term in both equations negative to each other.

Multiply equation (2) by
*x*-term in both equations negative to each other.

Add the equations (3) and (4) to eliminate *x*, as the coefficients of *x*-term in both equations are negative to each other

Precalculus: Mathematics for Calculus (Standalone Book)

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The Arch of a Bridge The opening of a railway...Ch. 10.6 - A Triangular Plot of Land An outdoors club is...Ch. 10.6 - DISCOVER PROVE: Determinant Formula for the Area...Ch. 10.6 - DISCUSS: Matrices with Determinant Zero Use the...Ch. 10.6 - DISCUSS WRITE: Solving Linear Systems Suppose you...Ch. 10.7 - For each rational function r, choose from (i)(iv)...Ch. 10.7 - For each rational function r, choose from (i)(iv)...Ch. 10.7 - Form of the Partial Fraction Decomposition Write...Ch. 10.7 - Form of the Partial Fraction Decomposition Write...Ch. 10.7 - Form of the Partial Fraction Decomposition Write...Ch. 10.7 - Form of the Partial Fraction Decomposition Write...Ch. 10.7 - Form of the Partial Fraction Decomposition Write...Ch. 10.7 - Form of the Partial Fraction Decomposition Write...Ch. 10.7 - Form of the Partial Fraction Decomposition Write...Ch. 10.7 - Form of the Partial Fraction Decomposition Write...Ch. 10.7 - Form of the Partial Fraction Decomposition Write...Ch. 10.7 - Form of the Partial Fraction Decomposition Write...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 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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