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How do I solve \(\text{SYSTEM OF EQUATIONS?}\) Look below to see the tutorial.

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All of us probably know one-variable equations. But, the two-variable linear equations may confuse people. In this tutorial, solving two-variable systems would be explained by substitution and elimination. \(\LARGE \color{MidnightBlue}{\text {SUBSTITUTION}}\) \(\Large \color{purple}{\rightarrow 0.45x +0.65y = 18.55 }\) \(\Large \color{purple}{\rightarrow x + y = 35 }\) Okay, now let's take any of the variables. Let's say x for the sake of convenience. Now, we just have to solve for x by subracting y from both sides, and we get: \(\Large \color{purple}{\rightarrow x = 35 - y }\) Now, we'll replace x with 35 - y, and we get: \(\Large \color{purple}{\rightarrow 0.45(35 - y) + 0.65y = 18.55 }\) Now, we can solve the equation easily. \(\Large \color{MidnightBlue}{\text{ELIMINATION} }\) This one is again easy. You have to seek the possible ways. Let's solve the same system again! So, let's multiply the equation 'x + y = 35' by 0.45(both sides). We get: \(\Large \color{purple}{\rightarrow 0.45x + 0.45y = 15.75 }\) Subtract both equations: \(\Large \color{purple}{\rightarrow (0.45x - 0.45x) + (0.65y - 0.45y) = 19.25 }\) \(\Large \color{purple}{\rightarrow 0.20y = 19.25 }\) \(\Large \color{purple}{\rightarrow y = 96.25 }\) Now, we can just solve for x because we know the value of y.
@ParthKohli Is this "Tutorial" called "Collecting medals" ? lol

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Other answers:

i think we need a separate section for these
@satellite73 Exactly what I think.
So we can copy and paste a link and tell the asker to come back if he/she still had more questions after reading the tutorials @satellite73
your tutorial is fine as is, but its missing a few important pointers. The "why" it works would be helpful. And also if you could explain the 3 possible results that can occur. The notion that we can find infinite or no consistent solution is something that tends to confuse people. And the knowledge of why these outcomes are possible explains those mysteries.
@ParthKohli excellent work! I appreciate it.
@amistre64 I'd certainly take care of that in the future. @2bornot2b Thank you :)
This tutorial might turn out to be quite helpful for someone searching the internet for "how to solve simultaneous equations". @amistre64 I believe parthkohli prepared it for high school level, therefore he decided to exclude that part.
@2bornot2b I don't know if it's high school or not, but considering that the person knows one-variable linear equations, I posted it.
You forgot one important thing. First of all, you said system of equations. You need to limit that down to first degree 2 varibles determined. Second of all, you forgot cramers rule. Other than that, good enough.
*2 imporant things
Did you know that you can reduce AES encryption down to a "system of equations"? You claimed to solve that, xD
@inkyvoyd Yes, about the Cramer's rule, I have written on the top line that I will explain it using only substitution and elimination. You see, these are two simple methods. It'd have taken hours if I'd used the cramer's rule and graphs.
Actually, cramer's rule was the fastest way to program the system of equation's solution.
^^ No.
isnt's cramer's rule linear algebra o.O
i like gauss-jordan elimination for the record :p
Well, my graphing calculator says so.
Computing determinant is itself tedious.
Well, programming a computer algebra system is more tedious -.-
When you will study numerical analysis you will understand what I meant :)
I will never study numerical analysis, and I will never understand zzz
(Neither will my Ti-84Plus SE)
since they said the good comments already i'll be the "simon cowell" from a tutor to another one. 1) You should solve the SUBSTITUTION and ELIMINATION methods thoroughly not just end in the middle 2) You did not state WHY you multiplied 0.45 in the ELIMINATION method. 3) Inconsistency. In the ELIMINATION method you solved for y. You did not solve for y in the SUBSTITUTION method though. and again, you cut in the middle 4) You did not prove that the results of the SUBSTITUTION method and the ELIMINATION method were the same. that are all my bad comments...otherwise it was good :) deserved the medals ^_~
Want to see my tutorial? The answer is always no. I just bother people until they see it, then they just give medals and leave. :/ @lgbasallote
They never provide feedback!
one more thing... "Okay, now let's take any of the variables. Let's say x for the sake of convenience. Now, we just have to solve for x by subracting y from both sides" be more did not state which you used, if first equation or second equation..although that is pretty obvious when looked at the next step, these things should still not be omitted. @inkyvoyd honestly...a lot of us do not know what you're saying :p haha no offense
What I'm saying? look at my link! LOOOOL

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