Weekly Math Problem #55

System of Linear Equations. I know it has been a while since the last problem (of which I still owe you my solution 🥴...it's coming, it's coming). Please don't disown me. When life throws you curveballs, you learn how to catch 'em. ⚾️🤷🏿‍♀️ ...And, I'm still learning how to catch. 

So, to get my feet wet, I'm starting with the problem below. To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     Methods for solving a system of linear equations
        

WMP! #55 says to...

Happy solving!

Check back on Friday, September 17th for the solution, which will be posted below ⬇️.

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Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 Solution Time! 📓✏️

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I went through my blog to see which WMPs already involved this week's topic. So,  check out WMP! #4 and WMP! #28 to how I solved those systems. WMP! #4 is more similar to this week's problem than WMP! #28 is. 

Just as a reminder, you have multiple options to use when deciding how to solve the system--addition/elimination method, substitution method, and Guassian elimination (if you're feeling fancy 😉). I am going to go ahead and do the substitution method. The first thing I do is label my equation. This helps me to keep track of things.

Next, I need to examine the equations to see which methods I want to move forward with. For the fun of it, I've decided to do the substitution method. Equations (A) and (B) both possess variables with "1" coefficients. Since equation (A) has a variable with a positive 1 coefficient, I'll just work with that. 

I isolate the variable and label the rearranged version of the equation:

Now, I will substitute this equation into the other two original equations (B) and (C). This allows me to reduce the variables--going from three variables down to two. 

After substituting and simplifying, I have a system of two linear equations in two variables. I examine this system and proceed with the substitution method again. Repeating a similar process from above.

Once this round of substitution is complete, I have come up with a value for one of the variables. Moving forward with with backward substitution...lol...I am able to find the values for the remaining variables and present my solution.

As you may know with mathematics, getting an answer doesn't mean that it's correct. So, I checked my solution in the original system to make sure that it works completely.

Thanks for hanging with me this week. It feels good to get back into the swing of things. 

▪️ What is your preferred method for solving a system like the one from this week's problem??

▪️ Let me know what you thought about this week's problem in the comments section. 

Thanks for sticking around and solving with me this week!

Up next, WMP! #56. 👍🏿

Cheers!

The Younge Lady

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 ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee: TheYoungeLady

✏️📓 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

Weekly Math Problem! #4

System of Linear Equations. Typically, when you've encountered this topic in learning math, you've either encountered a system of two linear equations with two unknowns (from an algebra course), or a system of three linear equations with three unknowns (from a college algebra course). I don't recall ever having to solve a system of four linear equations with four unknowns, however, when I saw it I knew that I would be able to solve it. I knew what I needed to do.

Depending on what level of math you've completed, you're aware that you have a few options when it comes to solving a system of four linear equations with four unknowns. To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  Methods for solving systems of linear equations

    ✔️  How to row reduce a matrix

Here goes WMP! #4... 

Happy solving! Check back on Friday, May 29th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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So, I thought it would be cool to solve this problem two ways--using the elimination method and by using Guass-Jordan elimination on the corresponding augmented matrix--just to compare how they look and see how many steps each requires to solve in completion.

Elimination Method

Guass-Jordan Elimination Method

The elimination method definitely required less steps as compared to the Guass-Jordan elimination method. As you can see, when done correctly, either method will yield the same solution. 👍🏿 The substitution method can also be used. I must say, there was something strangely sort of calming from row reducing the matrix. But then again, I'm not your typical person. 🤷🏿‍♀️ I definitely plan on having a problem from linear algebra for an upcoming WMP!  

 

◾️ Did my solution match yours?? 

◾️ Which method do you prefer when solving a system of four linear equations with four variables??

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

See you soon for WMP! #5 😉😁

Cheers!

The Younge Lady