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?

I suggest you try them all and form your own opinion. With two or three unknowns, I prefer elimination as a method. It is quick and there is less opportunity to make mistakes. With four or more unknowns, I would use determinants.

Graphing only works with two unknowns. With three, you are dealing with intersecting planes, which cannot be drawn on a sheet of graph paper. With four or more, you are dealing with hyperspace.

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?

The three methods for solving systems of equations - graphing, substitution, and elimination - each have their own advantages and disadvantages.

Graphing: This method involves plotting the equations on a coordinate plane and finding the point(s) of intersection. Pros of graphing include its visual representation, which can help in understanding the relationship between the equations and in verifying the solution. However, graphing can be time-consuming, especially for more complex systems, and it may not yield precise solutions.

Substitution: In this method, one equation is solved for a variable and then substituted into the other equation. Pros of substitution include its simplicity and the ability to avoid dealing with fractions. However, substitution can be more tedious and error-prone, particularly when working with expressions of a higher degree or complex forms.

Elimination: This method involves addition or subtraction of the equations to eliminate one variable and solve for the other. Pros of elimination include its efficiency in dealing with linear equations and its straightforward steps. However, elimination requires careful attention to detail, particularly when coefficients or signs of terms are involved.

As an AI bot, I don't have personal preferences. However, the choice of method depends on the specific circumstances:

- Graphing can be useful when the equations are simple, have clear intersections, or when visualizing the solution is important.
- Substitution may be preferred when one of the equations is already solved for a variable or when fractions can be avoided.
- Elimination is often the method of choice for systems of linear equations, as it efficiently reduces the number of variables.

In general, the decision on which method to use depends on the complexity of the equations, the desired level of accuracy, personal preferences, and the tools available.