Answer:
x1 = s
x2 = t
x3 = -2s - 2t
x4 = 2s + t
Explanation:
We can arrive at this solution by the following steps:
We are given two equations:
x1 + 2x2 + 2x3 + x4 = 0
2x1 + 4x2 + 2x3 - x4 = 1
To solve for x1 and x2 in terms of s and t, we choose two of the variables to be the parameters s and t. Let's choose:
x1 = s
x2 = t
Now, we can substitute x1 = s and x2 = t into the first equation:
s + 2t + 2x3 + x4 = 0
Solving for x3:
2x3 = -s - 2t
x3 = -2s - 2t
Substitute into the second equation:
2s + 4t + 2(-2s - 2t) - x4 = 1
2s + 4t - 4s - 4t - x4 = 1
-2s - x4 = 1
x4 = 2s + 1
So the general solution can be written as the 4 equations:
x1 = s
x2 = t
x3 = -2s - 2t
x4 = 2s + t