Switch the first two equations:
w + x - y + 2z = 1
2w - x + y - z = 1
3w + z = 2
3w - 3x + 3y - 4z = 1
Multiply equation 1 by -2 and add the result to equation 2
Multiply equation 1 by -3 and add the result to equation 3
Multiply equation 1 by -3 and add the result to equation 4:
w + x - y + 2z = 1
-3x + 3y -5z = -1
-3x + 3y - 5z = -1
-6x + 6y - 10z = -2
Multiply equation 2 by -1 and add the result to equation 3
Multiply equation 2 by -2 and add the result to equation 4:
w + x - y + 2z = 1
-3x + 3y - 5z = -1
0 = 0
0 = 0
-3x = -3y + 5z - 1 So, x = y - (5/3)z + 1/3
From the first equation, w = -(y - (5/3)z + (1/3)) + y - 2z + 1 = -(1/3)z + 2/3
Solution set:
x = y - (5/3)z + 1/3
w = - (1/3)z + 2/3
y and z are arbitrary real numbers
For example, if y = 1 and z = 3, then x = -11/3 and w = -1/3
