System of equation can be solved by graphing or by using substitution or elimation. What are the pros and cons for each methods?
Since this is not my area of expertise, I searched Google under the key words "math substitution elimination compare" to get this:
http://www.google.com/search?client=safari&rls=en&q=math+substitution+elimination+compare&ie=UTF-8&oe=UTF-8
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
When solving a system of equations, such as two or more simultaneous equations, there are various methods available, including graphing, substitution, and elimination. Each method has its advantages and disadvantages, depending on the specific problem at hand. Let's discuss the pros and cons of each method:
1. Graphing Method:
- Pros:
- Visual representation: Graphing equations allows you to see the intersection (or absence thereof) of the lines, providing a clear visual understanding.
- Intuitive approach: Graphing can be particularly useful when solving simple systems, as it provides a straightforward method to identify the solution.
- Cons:
- Precision: Depending on the accuracy of the graph, finding the exact solution may be challenging, especially if the intersection point has decimals or is not easily determined.
- Limited to two variables: Graphing becomes increasingly complex as the number of variables increases, making it less practical for larger systems.
2. Substitution Method:
- Pros:
- Simplification: Substitution can often lead to fewer variables to deal with, reducing the complexity of the problem.
- Flexibility: This method can be used for any number of variables, making it applicable to a wide range of systems.
- Cons:
- Lengthy calculations: When substitution involves multiple steps or requires solving equations containing complex expressions, it can become time-consuming.
- Potential for errors: Repeated substitution can increase the likelihood of computational mistakes, especially if the equations are lengthy.
3. Elimination Method:
- Pros:
- Simultaneous elimination: This method allows you to eliminate variables by adding or subtracting the equations, simplifying the system.
- Well-suited for linear equations: Elimination is particularly efficient when working with linear equations, as it eliminates one variable at a time.
- Cons:
- Complex coefficients: If the coefficients of the variables are large or contain fractions, elimination may result in unwieldy calculations.
- Limited to specific systems: Elimination works best when the equations are linear and have coefficients that can be easily manipulated.
In summary, the choice of method depends on the specific characteristics of the system of equations. Graphing provides a visual representation but may lack precision for complex systems. Substitution offers flexibility but can be time-consuming. Elimination is efficient for linear equations but may be limited to specific types of systems.