Question 1196448
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<pre>

2x1 + x2 - x3 + 2x4 = 10
-x1 - 3x2 + x3 - 5x4 = -11
3x1 + 5x2 - 3x3 + x4 = 35
-4x1 - 2x2 - 3x3 - x4 = 2
 
We rewrite the system of equations in matrix form and solve it using the Gauss method

2	1	-1	2	10
-1	-3	1	-5	-11
3	5	-3	1	35
-4	-2	-3	-1	2
 
Divide the 1st row by 2

1	0.5	-0.5	1	5
-1	-3	1	-5	-11
3	5	-3	1	35
-4	-2	-3	-1	2
 
to line 2 we add line 1 multiplied by 1; from line 3 we subtract line 1 multiplied by 3; 
to line 4 add line 1 multiplied by 4

1	0.5	-0.5	1	5
0	-2.5	0.5	-4	-6
0	3.5	-1.5	-2	20
0	0	-5	3	22
 
Divide the 2nd line by -2.5

1	0.5	-0.5	1	5
0	1	-0.2	1.6	2.4
0	3.5	-1.5	-2	20
0	0	-5	3	22
 
from line 1 we subtract line 2, multiplied by 0.5; from line 3 subtract line 2 multiplied by 3.5

1	0	-0.4	0.2	3.8
0	1	-0.2	1.6	2.4
0	0	-0.8	-7.6	11.6
0	0	-5	3	22
 
Divide the 3rd line by -0.8

1	0	-0.4	0.2	3.8
0	1	-0.2	1.6	2.4
0	0	1	9.5	-14.5
0	0	-5	3	22
 
to line 1 we add line 3 multiplied by 0.4; to line 2 add line 3 multiplied by 0.2;
to line 4 add line 3 multiplied by 5

1	0	0	4	-2
0	1	0	3.5	-0.5
0	0	1	9.5	-14.5
0	0	0	50.5	-50.5
 
Divide the 4th line by 50.5

1	0	0	4	-2
0	1	0	3.5	-0.5
0	0	1	9.5	-14.5
0	0	0	1	-1
 
from line 1 we subtract line 4, multiplied by 4; from line 2 we subtract line 4, multiplied by 3.5;
from line 3 subtract line 4 multiplied by 9.5

1	0	0	0	2
0	1	0	0	3
0	0	1	0	-5
0	0	0	1	-1
 
x1 = 2
x2 = 3
x3 = -5
x4 = -1
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Solved.