I sent my professor asked the pros and cons of each method, I answered with this;
When graphing; pros are that graphing gives you a picture of what the solution is. Cons would be is that graphing is not always accurate and it is difficult to see the location of the points. (Another problem I have personally is graphing the points backwards.) When using substitution; pros are that the solution is more accurate. Cons are that there would be multiple solutions for an equation. Elimination pros would be that it works for almost every equation. Cons would be that although some believe it to be easier, I find it more difficult to do because I do not always know what to eliminate. I like the substitution method best because I can use whichever number I would like for the variable to solve the problem. If the equation had many variables I would use elimination because this would be easier then substituting.
She than responded back to me with this;
Hi Diana, You did a great job explaining each method. You graphically described each situation that can occur when solving systems of equations. Can you classify each situation?
My question is what does she mean by classify each situation? Does she want an example of each situation?
They say that Lynn's professor is still waiting for Lynn's answer...
When your professor asks you to "classify each situation," it means she wants you to categorize or group the different situations that can occur when solving systems of equations using different methods.
To classify each situation, you can provide examples of when each method is most suitable or effective. For instance:
1. Graphing method:
- Situation: When the system of equations consists of two linear equations with distinct slopes.
- Example: y = 2x + 3 and y = -3x + 2
2. Substitution method:
- Situation: When one of the equations is already solved for a variable.
- Example: x = 2y - 3 and 3x + 4y = 10 (where x is already isolated in the first equation)
3. Elimination method:
- Situation: When the coefficients of one variable in both equations are easy to eliminate.
- Example: 2x + 3y = 5 and 4x + 6y = 8 (where multiplying the first equation by 2 and the second equation by -1 will cancel out the variable x)
By classifying each situation, you are providing specific scenarios where each method would be most appropriate and highlighting the benefits or advantages of using them.