The solution x, = and x, can be read from the resulting system. Thus, the system has a unique solution. To show that the given system of equations has an infinite number of solutions for r=2, begin by substituting r=2 into each equation, and then collect all variables terms on the left side. 3x, - 4x2 = 2x4 X1- 2x2 = 2x2 (Simplify your answers) Next, eliminate x, from the second equation. Adding times the first equation to the second equation changes the second equation to (Simplify your answers.) Interpret the resulting system of equation. Choose the correct answer below and complete the corresponding answer box(es) to complete your choice. (Simplify your answers.) O A. The first equation implies that x, and the second equation mplies that X, = Since these answers are not equal, no free variables exist. Therefore, the system has an infinite number of solutions. O B. The first equation implies that x,= but there is no equation for x, Evidently, x2 is a free variable and any value can be assigned to it. Therefore, the system has an infinite number of solutions. O C. The first equation implies that x, Since these answers are equal, a free variable exists. Therefore, the system has an infinite number of solutions. and the second equation implies that x,
The solution x, = and x, can be read from the resulting system. Thus, the system has a unique solution. To show that the given system of equations has an infinite number of solutions for r=2, begin by substituting r=2 into each equation, and then collect all variables terms on the left side. 3x, - 4x2 = 2x4 X1- 2x2 = 2x2 (Simplify your answers) Next, eliminate x, from the second equation. Adding times the first equation to the second equation changes the second equation to (Simplify your answers.) Interpret the resulting system of equation. Choose the correct answer below and complete the corresponding answer box(es) to complete your choice. (Simplify your answers.) O A. The first equation implies that x, and the second equation mplies that X, = Since these answers are not equal, no free variables exist. Therefore, the system has an infinite number of solutions. O B. The first equation implies that x,= but there is no equation for x, Evidently, x2 is a free variable and any value can be assigned to it. Therefore, the system has an infinite number of solutions. O C. The first equation implies that x, Since these answers are equal, a free variable exists. Therefore, the system has an infinite number of solutions. and the second equation implies that x,
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 76E
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage