Your favorite math magazine has recently published an article on their website about whether solving systems of non-linear equations is easier by graphing or algebraically.

You decide to write an email to the editor of the math magazine defending your opinion.

Your email must be two to four paragraphs in length.
You must express your opinion on which method is easiest.
Provide at least three pieces of supporting evidence.
Provide an additional graph of a system of non-linear equations that supports your viewpoint.

Question

Your favorite math magazine has recently published an article on their website about whether solving systems of non-linear equations is easier by graphing or algebraically.

You decide to write an email to the editor of the math magazine defending your opinion.

Your email must be two to four paragraphs in length.
You must express your opinion on which method is easiest.
Provide at least three pieces of supporting evidence.
Provide an additional graph of a system of non-linear equations that supports your viewpoint.

anonymous · Answer

@ranga

ranga · Answer

With the advent of graphing calculators and the availability of free online graphing websites my opinion is graphing will probably be easier in solving many system of non-linear equations. Other than quadratic equations and some simple set of non-linear equations, algebraic solution may not even be possible for many complicated set of non-linear equations. For example, it may not be possible to solve the following set of two non-linear equations algebraically: x^2 + y^3 = 10 and y = 5sin(x+1). Also, in algebraic method, there is a possibility of introducing extraneous solutions. Therefore, each solution must be checked with the original set of non-linear equations to make sure they satisfy the equations. But in graphical method we will be looking at the points of intersection of the graphs and they will be the solutions and not extraneous solutions. Three pieces of supporting evidence: Three examples of non-linear equations that are very difficult or impossible to solve algebraically but can be solved relatively quickly with the aid of a graphing calculator: y = -2x^3 - 5x^2 + 6x + 1 and y = x^5 - 4 y = e^x and y = x^3 + 4 y = sqrt(x+10) and y= x^2 - 3 Provide a graph: We solving the following two non-linear equations by graphing: x^2 + y^3 = 10 and y = 5sin(x+1). The plot is shown in the link: http://www.wolframalpha.com/input/?i=plot+x^2%2By^3%3D10%3B+y+%3D+5sin%28x%2B1%29 The red dots are the intersection points. Position the cursor on the red dots gives us the following points of intersection and they are the solutions: (-3.81, -1.65); (-0.56, 2.13), (1.75, 1.91)

anonymous · Answer

Thank you @ranga so much for your help!

anonymous · Answer

I'm sorry I couldn't reply to you earlier. I had to do some errands! Wow, you are truly amazing! @ranga and once again THANK YOU!