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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✏️📓 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