I understand that systems of equations can be solved by graphing or by using substitution or elimination. But I cannot think of any pros or cons so...

What are pros and cons of each method?

Mathematical solutions to systems of equations are more accurate than graphical solutions; because when the point of interception fall between grid lines, you must estimate the point location. Which is easier the elimination method or the substitution method? Well, it depends on the equations. Most of the time I use the elimination method. But sometimes I find it easier to use the substitution method. If one of the equations has only one unknown, I use the substitution method. Most of the time it will depend on the individual.

eat my crum

Great question! Let's go through each method and discuss their pros and cons:

1. Graphing:
Pros:
- Visual representation: Graphing allows you to see the intersection point(s) of the equations on a coordinate plane, which can provide a clear picture of the solution.
- Intuitive: It doesn't require any algebraic manipulation, making it accessible even to those who are not comfortable with algebra.

Cons:
- Approximate solutions: Graphing can sometimes lead to imprecise solutions as it relies on the accuracy of plotting points and drawing lines.
- Time-consuming: Graphing can be time-consuming, especially if the equations have complicated forms or if there are multiple variables involved.

2. Substitution:
Pros:
- Straightforward procedure: Substitution involves solving one equation for one variable and then substituting that expression into the other equation. It can be a more systematic and sequential approach to solving systems of equations.
- Flexible: Substitution can be utilized regardless of the format or complexity of the equations.

Cons:
- Complexity in variables: When working with equations involving multiple variables, substitution can result in complex expressions that might be challenging to work with.
- High chance of errors: Substitution requires careful substitution of one equation into another, which means there's a greater chance of making algebraic mistakes.

3. Elimination:
Pros:
- Simplification: Elimination involves adding or subtracting the equations in a way that eliminates one variable, leading to a simpler equation with just one unknown.
- Good for linear systems: Elimination is well-suited for systems of linear equations since it involves the addition or subtraction of variables with equal coefficients.

Cons:
- Requires manipulation: Elimination often requires manipulating equations to make coefficients or terms cancel out, which can be more algebraically involved.
- Limitations in nonlinear systems: Elimination can become more challenging or even impossible when dealing with nonlinear systems of equations.

It's important to note that the most suitable method may vary depending on the specific system of equations, personal preference, and the tools you have at your disposal.