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?

Personally, I like gaussian reduction as a choice method, becausing my TI83 does it very quickly and accurately.

But for your methods, graphing on a graphing calc is fast. In school, often variables are assigned whole number values, which make elimination easy, but in real life (engineering), few answers are even rational numbers, much less whole numbers.

Graphing, substitution, and elimination are all methods used to solve systems of equations. Each method has its own pros and cons.

Graphing involves graphing the equations on a coordinate plane and finding the point(s) of intersection. It is a visual method that can provide a clear understanding of the solution. However, it may not be precise, especially if the intersection point is not easily determined from the graph. Additionally, graphing can be time-consuming and impractical for complex systems with multiple equations.

Substitution involves solving one of the equations for a variable, and then substituting that expression into the other equation(s). It is a straightforward method that can be used for any system of equations, regardless of complexity. However, it can be tedious and involve many steps, especially if the equations are not easy to manipulate algebraically.

Elimination involves adding or subtracting equations in order to eliminate one variable and solve for the remaining variables. It is often the most efficient method for systems in which the coefficients of one of the variables can easily be made to cancel out. However, it can be challenging and time-consuming for systems with large coefficients or complex equations.

As an AI bot, I do not have personal preferences. Each method has its own advantages and disadvantages, and the choice of which method to use depends on the specific circumstances.

- Graphing may be preferred when the solution is easily visible on the graph or when a visual representation is necessary.
- Substitution may be preferred when the equations are simple and easy to manipulate algebraically, or when other methods appear impractical or time-consuming.
- Elimination may be preferred when the coefficients are simple to manipulate and can easily be canceled out, or when the system is large and substitution would involve too many steps.

It's important to consider the complexity of the system, the available resources (such as graph paper or a calculator), and personal preference or familiarity with each method to determine which one is best suited for a given situation.