How can I solve this system of equations? I've tried all night and all day but I get nowhere every time

use a matrix fuckturd
werks errytime

EDIT with first line.
[math]a=99-b-2c[/math]. Not sure why I squared that.

There are several ways to solve systems of equations using linear algebra.
If you can give me the name of a method I can use here, I'd like to fucking hear it.

Okay bois, pure mathematics freshman coming the fuck in to solve this or you.

Let me get this clear:

First take the equation

[math] a^2=b^2+2c^2+2c+1 [/math] and use your IQ to reduce:

[math] a^2 - b^2 =2c^2+2c+1 [/math]

which then, through harder IQ power becomes

[math] (a+b)(a-b) = 2c^2+2c+1 [/math]

That is our first equation in what I like to call, non-brainlet form. That is to say, it will yield a solution.

Then take [math]a+b+2c=99[/math] and also put in non-brainlet form to get
[math] a+b = 99 - 2c [/math]

Now we have a form for a+b so now replace
[math](99 - 2c)(a-b) = 2c^2+2c+1[/math]

which yields

[math](a-b) = \frac{2c^2+2c+1}{99 - 2c} [/math]

Now add this on top of our equation for a+b to get

[math]2a = \frac{2c^2+2c+1}{99 - 2c} + 99 - 2c [/math]

which then becomes

[math]a = \frac{\frac{2c^2+2c+1}{99 - 2c} + 99 - 2c}{2} [/math]

And then, repalcing in one of our equations for a + b to get

[math]b = 99 - 2c - \frac{\frac{2c^2+2c+1}{99 - 2c} + 99 - 2c}{2} [/math]

Then obviously [math] d = c + 1 [/math]

and c is our free variable

Plugging in c=0 we get d=1, a=49.50505050...
b = 49.49494949...

You can try it out.

There are 3 unknowns since d is given as a function of c.

OP here. Absolutely genius mate. Props for knowing your shit unlike some people here.
Where do you learn these techniques? I'm also studying pure mathematics (2nd year) but this seems like some serious out of the box thinking.
I got this problem from a stupid word puzzles book last night. Finally got some closure now. Cheers.

No problem. I would have solved it earlier but I was playing overwatch with a friend, but then he left me because he got hungry so I decided to attack the beast.

>Where do you learn these techniques?

Well, if you notice I really didn't use any technique or theorem. But I think the most important part was when I decided to get an equation for (a+b)(a-b) and my logic there was that if calculus has taught me anything, it is that products are good, sums are bad, so take everything you have and somehow turn it into a product. So call it the "instinct to turn everything into a product" technique.

After that the pieces started falling together.

Yeah I hear ya man. While playing around with it I actually got to that [math](a+b)(a-b)[/math] term but didn't think to do much with it.

dude there all lines on the graph

what is a line

what is a linear equation

>what is a linear equation

A linear equation is one where all the terms are... linear? So what about this one, dummy: [math]a^2=b^2+c^2+d^2[/math]

This is not a linear algebra problem, it is an algebra problem.

Also, I already found the solutions here and they turn out to be infinitely many.