Every Algebra Student MUST Know This to PASS!

How to two variable linear system.

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TC Math Notes

[tomtke]

The generic rule that sticks in my mind is: to solve for TWO unknowns requires TWO equations.

For instance : "if one fence is twice as tall as another AND the tall fence is two feet taller, how tall are both fences " These are two equations with two unknowns.

F-tall = 2•F-short (1)
F-tall - F-short = 2 (2)

substituting 1 --> 2

F-tall = 2•F-short (1)
2•F-short - F-short = 2
F-short = 2

further, putting F-short = 2 into (1)
F-tall = 2•F-short (1)
F-tall = 2 • 2
= 4

for three unknowns requires three equations... 4 requires 4... 5, 5 etc.

And Y E S this is must know for algebra!

[johnplong]

John is absolutely right YOU HAVE to Be Good at talking Math Notes If you are having problems understanding Sit in the front of the class

[skilz]

Did it in my head, a = 6, b = -2

(1/2)a - b = 5
a + b = 4

Is what is given. The simplest way to do this is by adding the two equations together that gives us:

3a/2 = 9 and now we can solve for a since b was cancelled from the equation giving us a = 6.

We can now take a=6 and plug that back into either of the origin equations to solve for b. I'll use the 2nd since it's the easiest.

6 + b = 4 and solving for b gives us - 2. Now we can take both a=6 and b = -2 and plug it back into the first equation to test to see if we ended up with the right solution.

(1/2)*a - b = 5
(1/2)*6 -(-2) = 5
3 + 2 = 5
5 = 5. Yes, a = 6 and b = -2.

[mr.mxyzptlks]

I am going to with “System” of linear equations, in this case of 2 variables. Was tempted to say “Set”, but that will have a very different, and specific, meaning later on 😊

[devonwilson]

Greetings. With reference to equations given, we will first rewrite equation 1 as a -2b= 10. Thereafter, we will subtract equation 2 from the rewritten equation 1 to get negative 3b = 6. Therefore, b = -2 after dividing both sides by negative 3. With having determined the value of b, we will now substitute this value into equation 2, ( a+b = 4). The result will be a +(-2) = 4 and a -2 = 4 leaving us with a = 4 +2 =6. The values for a and b are 6 and negative 2, respectively.

[jjeeqq]

I have problem, how do i solve T for this equation?:

R=(C+T)/(C+T/9)

I did it once but now i can't do it anymore :D
Spoiler alert for answer:

T=9*((C*R-C)/(9-R))

But i don't know how i ended up to it.
This is my own rocket equation: R is fuel ratio vessel full/empty. C is cargo+Weight of engines. T=fuel tanks full weight and empty fuel tank is T/9.

[dannyroosenboom]

i could only fugure out that either a or b must be a negative number but i don't know yet how to figure out wich one. i like to think first nefore gibing up and listen to your explanation. to me it seems like b must be the negative number

[zypation]

This is kind of like multi step equation kinda confusing at the start but I'm getting the hang of it

[comicus]

I have been looking at some of your videos in passing just to see how much I remember after nearly half a century. This particular problem reminds me of a similar one that I still remember after all those years. It is a bit trickier since you have to figure out the second equation. A man's and his wife's ages added together = 98. He is twice as old as she was when he was the age she is today. Find their ages. Show your work!

[devonwilson]

Greetings. This seems somewhat tricky. However, there is nothing tricky about the problem. First, you can find 3% of 900 and thereafter find 2% of the result to get .54. Alternatively, you can do 2% of 3% to get 6/10, 000 and thereafter multiplying this result by 900 to the value, .54.

[joshuabradshaw]

I'm not so concerned about becoming a mathematics professor or nuclear physicist. What level of math do I need to get an accounting certificate, associates or bachelors degree? Algebra 2? I don't think I'll need geometry, calculus or trigonometry if I'm not going to be some kind of engineer or teacher.

[johnplong]

I did this using matrix Now the method you use I don’t remember “Ever be taught in High School or college Substitution is What I remember in Algebra This is Simply Algebra 1 stuff You do have to know this to pass and to move on to Algebra 2 you use what you learned in Algebra 1 in Algebra 2

[nickfraser]

2 equations two unknowns. I won't insult you by going through the process, a = 6 and b= -2

[devonwilson]

Greetings. I could not agree with you more in saying that " the best way to learn math is not just to have someone doing the work without you getting a grasp of what you are doing" . I have a friend that I have spent countless hours with in teaching basically the exact same accounting procedure over and over again just because the person does not try to learn but instead has always relied on me to do the work even it had absolutely nothing to do with me. I have made it clear over and over that, you have to do the work and also, it is not just about doing the work but more so to get an understanding of what is being done.

[johnplong]

I used determinants to solve this (6, -2)

[eparock]

i got the answer but i used the substitution method...

[panlomito]

Delicious brainpower was the only thing needed to solve this. 3/2a = 9 so a = 6 and b = - 2

[Geoff_G]

At the 10:00 mark you said to eliminate the b's but I know from Biology if we eliminate the bees all the people die.
🤪

[harrymatabal]

Sometimes i think what were you guys doing in school when you cannot solve simultaneous equations.

[bravobravoh]

Math is like any other language, the earlier in life that you learn it, the easier it will be to understand.