To solve: The given system of equations
Answer to Problem 19PPS
The system has infinitely many solutions.
Explanation of Solution
Given Information:
The system of equations
Formula Used
Here, three equations with three unknown variables are given. The approach used is variable elimination and simplification.
(1) First two equations are multiplied with a factor such that one of the variables has identical coefficients.
(2) Add the modified equations to eliminate the particular variable.
(3) Then, the same process is repeated between any othercombination of two equations.
(4) This gives two equations with two unknowns which can be further solved by elimination.
(3) Substitute the obtained variable in one of the equations to get the second variable and then the third variable.
Calculation Here, the equations are,
Considering the first two equations, Multiplying each of the terms in equation (1) by-3, it becomes
Now, adding corresponding terms of (4) and (2) gives,
Now, multiplying each term in (1) by -4, the equation becomes,
Subtracting (6) from (3) ,
Subtracting (5) from (7) leads to
0=0
This implies the system has infinitely many solutions.
Chapter 3 Solutions
Glencoe Algebra 2 Student Edition C2014
Additional Math Textbook Solutions
Linear Algebra and Its Applications (5th Edition)
College Algebra
College Algebra (7th Edition)
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education