Extra credit math, i dont even know where to start

[MasterKung]

i know, i know, i should know how to do this, but i dont. can someone tell me a few ways to solve these

4w+x+2y-3z=-16
-3w+3x-y+4z=20
-w+2x+5y+z=-4
5w+4x+3y-z=-10

now i know if there were only two terms (such as only x and y) i could find one in terms of the other, set up one of the equations equal to x and put it in, yada yada. Now that there's four however I am not sure exactly what to do. I remember in algebra (two years ago) learning other ways to solve systems of equations but i don't remember exactly how its done, there's soemthing about adding them together, i don't know. this isn't exactly urgent(its extra credit) but if someone could help me out id really appreciate it. thanks.

 

[Ambitwistor]

The rough idea is to add them together to eliminate variables. For instance, if you multiplied the third equation by 4 and added it to the second equation, you'd have the sum

4w+x+2y-3z=-16
+ -4w+8x+20y+4z=-16

or

9x+22y+z=-32

thus eliminating w from that pair of equations. If you're systematic, you can get down to an equation that has just one variable in it. Then you can substitute it into an earlier equation with that variable and another to get a second variable, etc.

You can also look up "Gaussian elimination".

 

[ShawnD]

If you doing this in a class where do you not need to show HOW you got the answer, you can always just put them into a matrix on your calculator. I only know how to do it on a Texas Instraments calculator.
Go to matrix. Under edit, setup the number of rows x columns. Enter the coefficients. Go to home screen. Go to matrix. Go under math and go down to rref(. Go to matrix and hit enter on the matrix. Hit enter.

For the problem you gave, here are the answers:
W = -1
X = 1
Y = -2
Z = 3

 

[MasterKung]

thanks, i couldn't get that on my own, i kept trying to add them all together somehow, but it wasnt helping much. maybe now i can get it done.

[edit]oh, yeah, thanks for the calculator thing too, honestly id rather figure it out the long way, calculators are no fun [zz)][/edit]

 

[ShawnD]

Don't even lie. You would not want to do it the long way when dealing with static forces. Just last week I had to solve for 6 variables with 6 equations. Some of the coefficients were square roots and really big fractions...A few classmates did it long hand and it took at least an entire sheet of paper to do it.

 

[MasterKung]

yeah, but that's different, this is just extra credit, i bet along with that stuff you mentioned there was other work, or other things to do. all i have is this, and I am not sure whether i need to show work or not so i might as well, just to be on the safe side. but yeah, youre right, there are times when the calculator comes in handy.

 

[enigma]

Do this one long-hand, but learn to use the calculator.

There will come a time when even doing it with a calculator takes too much time, and you'll need to upgrade your techniques to PC.

 

[ShawnD]

Yeah, especialy if you take chemistry. In all the chemistry programs I've looked into, they all include some advanced computer work to do computations related to chemistry.