Think About It Consider the system of equations
(a) Find values for
(b) Explain how to solve the system in part (a) by the method of substitution and graphically.
(c) Write a brief paragraph describing any advantages of the method of substitution over the graphical method of solving a system of equations.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
College Algebra
Additional Math Textbook Solutions
Elementary Algebra
College Algebra (10th Edition)
EBK ALGEBRA FOUNDATIONS
Graphical Approach To College Algebra
Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
- Graphical Analysis. In Exercises 31-36, complete parts a-e for the system of equations. a Use a graphing utility to graph the system. b Use the graph to determine whether the system is consistent or inconsistent. c If the system is consistent, approximate the solution. d Solve the system algebraically. e Compare the solution in part d with the approximation in part c. What can you conclude? 14.7x+2.1y=1.0544.1x6.3y=3.15arrow_forwardTrue or False? In Exercises 69 and 70, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a A linear system can have exactly two solutions. b Two systems of linear equations are equivalent when they have the same solution set. c A system of three linear equations in two variables is always inconsistent.arrow_forwardProof Prove each property of the system of linear equation in n variables Ax=b. a If rank(A)=rank([Ab])=n, then the system has a unique solution. b If rank(A)=rank([Ab])n, then the system has infinitely many solution. c If rank(A)rank([Ab]), then the system is inconsistent.arrow_forward
- Discovery In Exercises 91 and 92, sketch the lines represented by the system of equations. Then use Gaussian elimination to solve the system. At each step of the elimination process, sketch the corresponding lines. What do you observe about the lines? x4y=35x6y=13arrow_forwardElectrical Network Applying Kirchhoff’s Laws to the electrical network in the figure, the currents I1, I2, and I3, are the solution of the system I1I2+I3=03I1+2I2=72I2+4I3=0 Find the currents.arrow_forwardWriting Consider the system of linear equations in x and y. a1x+b1y=c1a2x+b2y=c2a3x+b3y=c3 Describe the graphs of these three equations in the xy-plane when the system has a exactly one solution, b infinitely many solutions, and c no solution.arrow_forward
- True or False? In Exercises 69 and 70, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a A system of one linear equation in two variables is always consistent. b A system of two linear equations in three variables is always consistent. c If a linear system is consistent, then it has infinitely many solutions.arrow_forwardHomogeneous System In Exercises 65 and 66, find all values of the Greek letter lambda for which the homogeneous linear system has nontrivial solutions. (2)x+y=0x+(2)y=0arrow_forwardMathematical Modeling: A video of the path of a ball thrown by a baseball player was analyzed with a grid covering the TV screen. The video was paused three times, and the position of the ball was measured each time. The coordinates obtained are shown in the table. ( x and y are measured in feet.) (a) Use a system of equations to find the equation of the parabola y=ax2+bx+c that passes through the three points. Solve the system using matrices. (b) Use a graphing utility to graph the parabola. (c) Graphically approximate the maximum height of the ball and the point at which the ball struck the ground. (d) Analytically find the maximum height of the ball and the point at which the ball struck the ground. (e) Compare your results from parts (c) and (d).arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning