Question

Solve this system of equations.
6x-y+3z=-9
5x+5y-5z=20
3x-y+4z=-5

Answer 1

What do you know about solving systems of equations?

Answer 2

if you have n unknowns, you need n equations to solve them.
3 unknowns. 3 equations.

Answer 3

okay. That makes sense. would you mind walking me through it

Answer 4

Sure i suppose? You can subtract, add, multiply, divide, and do all kinda weird stuff to equations. you can also substitute for variables....

equation 2: 5x + 5y - 5z = 20. Divide 5 to all sides to get the simplest form
5( x + y - z) / 5 = 20 / 5 -> x + y - z = 4
Yay! It's in simple form now. Let's try adding this to some other equation and see what happens????

x + y - z = 4
3x -y + 4z = -5 Add the right sides and left sides together...
4x +y -y + 3z = -1
+ y - y gives us a zero so....
4x + 3z = -1 Now we have an equation of two unknowns, if you can find another, you can reduce also find both.

I dunno. Experiment with it. Add and subtract functions, the key is to eliminate some variables in the process, if you can reach the point where you have only variable, YOU FOUND IT! then you can subsitute it in the others and BAM! you get closer.

Answer 5

you could also use matrixes to solve this fast, but I dunno, I don't know of an algorithmic way to solve it all at once sadly. I'd experiment with it. Good luck!

Answer 6

Thank you, that makes sense!

Answer 7

http://www.mathplanet.com/education/algebra-2/matrices/using-matrices-when-solving-system-of-equations

^ This could help you. using matrices to solve these is super fast

Answer 8

https://www.mathsisfun.com/algebra/systems-linear-equations-matrices.html

This explains it well too

Answer 9

Just to check your work. Also all the steps are given thanks to WolframAlpha