Is there a case when you might prefer algebraically over graphically solving a system? Why or why not? Think about the type of possible solutions and how the method might affect your choice.

My answer: A case when I would prefer a algebraically would be trying to figure out how much my pay check would be if I got a new job. I would figure out the number of hours and times that by the hours I would work to determine the amount of money I would make each week. This would work better for me rather than making a graph. Making a graph would only be beneficial if I was comparing two differant jobs to see which one was better.

I think your answer looks fine. We are doing this in my school as well. The question is rather open for personal opinion, so as long as you can back it up, it is fine.

Sorry if this does not help

Your answer is a good example, but let me provide you with a more general explanation.

Algebraic methods and graphical methods are two different approaches to solving systems of equations. Each method has its advantages and may be preferred depending on the circumstances.

Algebraic solving involves manipulating equations algebraically to find the solution(s). This method is often preferred when you are looking for an exact solution or need to find the values of the variables algebraically. Algebraic methods can be very precise and provide a clear and concise solution. They can also handle cases where the equations are complex or have variables with multiple constraints.

Graphical solving, on the other hand, involves plotting the equations on a graph and finding the point(s) of intersection. This method is suitable when you want to visualize the solution or when you are interested in approximate values. Graphical methods are helpful for understanding the relationship between different variables and can give insights into the behavior of the system. They are also useful when dealing with simple equations or when a visual representation can provide a quick and intuitive solution.

The choice between algebraic and graphical methods depends on the nature of the system and the objectives of the problem. If precise values are required, or if the equations are complex, it may be more appropriate to use algebraic methods. On the other hand, if an approximate or visual understanding of the solution is sufficient, or if the equations are simple, then graphical methods may be preferable.

In summary, the type of possible solutions and the need for precision or visualization play a significant role in determining whether one should prefer algebraic or graphical methods for solving a system of equations.