Find the x, y z, & w?

Question

1x + 0y - 1z + 0w = -3
-2x - 1y - 2z -1w = -2
-2x + 0y + 2w + 3w = -3

So the anwser will be none

Answer 1

Try this:




This is a good system to solve using Gaussian Elimination:

(1)x + (0)y + (-1)z + (0)w = -3
(-2)x + (-1)y +(-2)z + (-1)w = -2
(-2)x + (0)y + (5)z +(3)w = -3

Simply write the coefficents of each equation (the numbers I have put in parentheses) in matrix form:

1 0 -1 0 : -3
-2 -1 -2 -1 : -2
-2 0 2 3 : -3

In row-reduced-echelon form this is:

1 1/4 0 0 : 7/4
0 1 4 0 : -5
0 0 0 1 : 1

(or in the form you are more familiar with)

(1)x + (1/4)y + (0)z + (0)w = 7/4
(0)x + (1)y + (4)z + (0)w = -5
(0)x + (0)y + (0)z + (1)w = 1

and the solution to your system is:

x = 7/4 - 1/4y
y = -5 - 4z
z = -5/4 - 1/4y
w =1

Which means there are infinitely many solutions.

If you are unfamiliar with this process, try the following links:

http://mathworld.wolfram.com/gaussianeli...
http://home.cc.umanitoba.ca/~ppenner/htt...

It is well worth the extra time to learn this handy tool now since it will make future systems much easier to solve. Best of luck!

Answer 2

This set of equations is unsolvable and infinite solutions. You can tell at first glance that with only 3 equations you can't solve for 4 unknowns.
Correct the third eqn and write the fourth one.

Answer 3

I'm not sure your last equation is correct.