o Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Which method do you like best? Why?

o What circumstances would cause you to use a different method?

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/.

For "math substitution method," I found:

http://www.google.com/search?client=safari&rls=en&q=math+substitution+method&ie=UTF-8&oe=UTF-8

Do the same for the elimination method and make your comparison.

it all depends upon the equations in question:

if equations are VERY straight forward then the graphing method can work
well. It has the advantage of visualation. In other words, you can see the behaviour of the system. Main drawback to graphing is it isnt very accurate for
solutions.

:
For other short and simple equations substitution can work well. The advantage to substitution is when one of the variables is already isolated in one of the equations. Even then you must look closely at the other equation to see how complicated the substitution method could be. A few drawbacks to substitution is there can be alot of division and finding LCM.
:
I would say the elimination method is the most popular and in my opinion is the best .Many times you can even do calculations in your mind, and so it is much faster. Elimination seems to be more useful when coefficients are larger, whereas substitution is useful when coefficients are smaller and when it is easy to islate a variable. Elimination works for any system of linear equations. After one or two steps you have a one-step equation to solve and you have half of your solution. Con can be Sloppy calculations can lead to incorrect solutions
If I need a rough idea of the solution, I graph. If one of the equations is already solved for y or for x, I use substitution. If neither of the above is true, I use elimination.

The pros and cons of each method for solving systems of equations are as follows:

1. Graphing:
Pros:
- It provides a visual representation of the system of equations.
- It allows for easy comparison of the two equations.
- It can provide an approximate solution quickly.

Cons:
- It may not provide an exact solution due to potential inaccuracies in plotting points.
- It can be time-consuming for complex systems.
- It may require a scale adjustment or extension of the graph if the solutions are not easily visible.

2. Substitution:
Pros:
- It allows for solving one equation in terms of a variable and substituting it into the other equation.
- It is generally straightforward to apply when one equation has a variable isolated.
- It can be more efficient for systems with complicated coefficients.

Cons:
- It might involve extensive algebraic manipulation, especially for higher-degree equations.
- It may become more complex if both equations require manipulation before substitution.
- It can be prone to algebraic errors.

3. Elimination:
Pros:
- It involves adding or subtracting the equations to eliminate one of the variables.
- It often leads to simpler equations to solve.
- It can be efficient for systems with coefficients that can be canceled out.

Cons:
- It might be more difficult to apply when both equations have the same variable coefficients.
- It may require multiplying one or both equations by constants, leading to larger numbers.
- It can be prone to errors during the elimination process.

The preferred method may vary depending on personal preference or the specific characteristics of the system of equations being solved. In general, the elimination method is often favored for systems with simple coefficients, while substitution is preferred when one equation involves an isolated variable.

Using a different method is typically necessary when one method becomes impractical or inefficient for solving a particular system. For example, if the system involves nonlinear equations or equations with complex coefficients, graphing may not be feasible. In such cases, substitution or elimination methods would be more appropriate. Similarly, if the system has one equation with a clear isolated variable, the substitution method may be the most efficient choice.

When solving systems of equations, there are multiple methods available, including graphing, substitution, and elimination. Each method has its own advantages and disadvantages, and the choice of which method to use largely depends on the specific circumstances and personal preference.

Graphing: This method involves plotting the equations on a graph and finding the point(s) of intersection, which represent the solution(s) of the system. The pros of graphing are that it provides a visual representation of the system and can help in identifying patterns or trends. It is relatively straightforward and can be useful for systems with simple equations. However, graphing can be time-consuming, especially for complex systems, and may not be accurate if the intersection point is not precise.

Substitution: In this method, one equation is solved for a variable, and then that expression is substituted into the other equation(s). The pros of substitution are that it can be used for systems with simple or complex equations, provides an algebraic solution, and can be more accurate than graphing. It also allows for solving systems where graphing is not feasible, such as when dealing with equations involving irrational numbers. However, substitution can become cumbersome if the equations involve large coefficients or complex expressions.

Elimination (also known as the addition/subtraction method): This method involves adding or subtracting the equations to eliminate one of the variables, allowing for the solution of the remaining variable(s). The pros of elimination are that it is efficient for systems with equations in standard form (Ax + By = C), especially when there are coefficients that can be easily canceled out. It can also be useful for systems with three or more equations. However, elimination can be challenging when coefficients are not easily eliminated, and it might not work well with equations involving fractions or decimals.

Personal preference plays a role in choosing the method. Some individuals may find graphing more intuitive, especially if they are visual learners. Others might prefer substitution or elimination, as they offer more algebraic manipulation and can be quicker for certain types of systems.

The choice of method may vary depending on the circumstances. For example:

- If the equations are simple and can be easily graphed, graphing can be a suitable method.
- If one of the equations is already solved for a variable or one variable can be easily isolated, substitution might be the most efficient method.
- If the equations are in standard form or involve large coefficients, elimination can be a preferred method.

Ultimately, the choice comes down to personal preference, the complexity of the equations, and the specific requirements of the problem at hand.