Solve following system of liner Equation

x1 + x2 + x3 + x4 = 0
x1 + x2 + x3 - x4 = 4
x1 + x2 - x3 + x4 = - 4
x1 - x2 + x3 + x4 = 2

Plz explain step by step

In first equation:
x1 = -x2 - x3 - x4

then we substitute that in second equation
(-x2 -x3 -x4) + x2 + x3 - x4 = 4
-2 * x4 = 4
x4 = -2

We go to the third
(-x2 -x3 -x4) + x2 - x3 +x4 = -4
-2 * x3 = -4
x3 = 2

Then the last equation
(-x2 -x3 -x4) -x2 +x3 +x4 = 2
-2 * x2 = 2
x2 = -1

x1 = 1 - 2 +2
x1 = 1

1) x1 + x2 + x3 + x4 = 0
Subtract
2) x1 + x2 + x3 - x4 = 4
-------------------------------
2x4 = -4
x4 = -2

3) x1 + x2 - x3 -2 = -4
x1 + x2 - x3 = -2
Add
4) x1 -x2 + x3 = 4
------------------------
2x1 = 2
x1 = 1
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2) 1 + x2 + x3 + 2 = 4
x2 + x3 = 1
3) 1 + x2 - x3 -2= -4
x2 - x3 = -3
adding 2x2 = -2
x2 = -1
Substitute in 1)
1 -1 +x3 -2 = 0
x3 = 2
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