SOLUTION: This was on a Hero's episode (Season 4, Episode 1) that never showed the solution, and thought I would place it up here as I came up with 2 answer myself, was wanting validation to

Question 985432: This was on a Hero's episode (Season 4, Episode 1) that never showed the solution, and thought I would place it up here as I came up with 2 answer myself, was wanting validation to my answer: (w=0,x=12/5,y=19/5,z=0) or (w=1, x=1, y=1, and z=1), the second set of answers I never actually worked out to be that, I just saw that answer automatically in my head, and it does indeed work, but I am unsure how to show the work for it, and would love someone to walk me through that if they wouldn't mind.
x + 2y + 3w + 4z = 10
2x - y + w - z = 1
3x + y + 4w + 3z = 11
-2x + 6y + 4w + 10z = 18

Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!

The determinant of the 4x4 matrix of this system is equal to zero.

So, the matrix is singular, actually.

Therefore, it is not amazing that you found two solutions of the system.

Indeed, there are infinitely many solutions.

The trick: I did not calculate the determinant myself.

I simply asked GOOGLE, and it pointed me to this solver (online calculator):
http://ncalculators.com/matrix/4x4-matrix-determinant-calculator.htm

I don't know why, but I trust to this result.

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