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? WHAT CIRCUMSTANCES WOULD CAUSE YOU TO USE A DIFFERENT METHOD?

Graphing is by far the hardest, UNLESS you have a graphing calculator, then its very easy. It all depends on how you want to work it. I cant really tell you the best way of doing it.

Graphing, substitution, and elimination are three common methods used to solve systems of equations. Each method has its own pros and cons, and the choice of method depends on various factors.

Graphing involves plotting the equations on a coordinate plane and identifying the point(s) of intersection as the solution(s). The pros of graphing are that it provides a visual representation of the system and allows for quick estimation and identification of solutions. However, graphing can be time-consuming, imprecise, and not viable for complex systems with multiple variables.

Substitution involves solving one equation for one variable and substituting it into the other equation(s). This method is useful when one of the equations is already solved for a variable. The pros of substitution are that it can be straightforward and relatively simple, especially when dealing with linear equations. However, substitution can be tedious and involve lengthy calculations, making it impractical for systems with many variables or complex equations.

Elimination involves manipulating the equations to eliminate one variable and solve for the remaining variables. This method is useful when the coefficients of one variable in both equations are additive inverses. The pros of elimination are that it can be efficient, especially when dealing with linear equations, and it simplifies the system and reduces variables. However, elimination may involve fractions, decimals, or large coefficients that can make calculations more challenging.

As an AI bot, I don't have personal preferences. However, the method I would recommend depends on the specific circumstances. Graphing is a good initial approach when the system is simple or there are only two variables. Substitution is preferable when one equation is already solved for a variable. Elimination is best when the coefficients of one variable are additive inverses or when simplification is desired.

To choose the most appropriate method, consider the complexity of the system, the coefficients involved, the number of variables, and the desired level of precision. It can also be helpful to try different methods if the initial one seems cumbersome or doesn't yield desired results.