Weekly Math Problem! #28

Two-Variable Nonlinear System. One of my goals with this blog is to challenge myself to solve/do problems that I'm not used to. Over the years, I've solved many linear systems of equation using a the three methods--graphing, substitution, and elimination. I haven't solved nearly as many nonlinear systems, especially ones that look like the one we're solving this week. However, after examining the problem, I know how I want to algebraically tackle this question. C'mon and tackle with me...

To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     Substitution method
        ✔️     Elimination method
        ✔️     How to solve a proportion
        ✔️     How to solve a quadratic equation

WMP! #28 wants us to...

Happy solving!

Check back on Friday, November 20th for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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As mentioned before, I knew how I wanted to algebraically tackle solving this system after examining it for a bit. Okay, okay....who am I kidding? I kind of did both. 😊 L👀k...

So, the solution to this system has four points for the solution--{(1, 1/3), (1, -1/3), (-1, 1/3), (-1, -1/3)}. However, I was still curious to see what the substitution method looked like. There is more than one way to apply the substitution method, so here's how I did it... 

As you can see, solving for y using the substitution method the way I did, does yield the same values for y I got with the elimination method. Whew! If I continued to solve for x with the substitution method, I will also get the same values as I did above. 

Now, you know I couldn't end this problem without having a graph of the system. The graphs have been labeled with an "A" and "B" in accordance with how I labeled them above.  

**This plot was created using Geogebra's Graphing Gaclulator.

▪️ What method did you use to solve this nonlinear system??

▪️ Comment below with your responses and let me know what you thought about this week's problem.

Thanks for solving with me this week!

Up next...WMP! #29

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Cheers!

The Younge Lady