To explain how the method of substitution differs from the method of elimination.
For added convenience, consider the case of system of equations involving only two variables.
Method of substitution in the case of linear equations involving only two variables:
Given a system of linear equations in two variables:
The method of substitution employs solving one of the equations, say
Now, this expression of
The value of
Now, the value of
Method of elimination in the case of linear equations in two variables:
The method of elimination employs the elimination of one variable from the system of equations. Thus, the first step is to determine the variable that is to be eliminated. Then, the equations are multiplied with different non-zero constants and added together in a way so that the targeted variable is eliminated. In some cases, a simple addition would eliminate the variable. But, in general scalar multiplication is needed as said earlier.
After finding the value of the non-eliminated variable, it is substituted into any of the equations to find the value of the other one.
Comparing and contrasting the methods, the method of substitution is based on substitution and that of elimination is based on elimination.
In the method of substitution, unlike eliminating a variable, a variable is isolated from one of the equations. Then, it is substituted into the other equation and solved to find the value of the other variable. Then onwards both the methods follow the same way. The method of substitution involves more steps as compared to the method of elimination. But, it seems like a concrete approach to solve any system of equation.
Chapter 3 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
- 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