(Solution) - Use the computer to solve these systems from the first -(2025 Original AI-Free Solution)

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Use the computer to solve these systems from the first subsection, or conclude 'many solutions' or 'no solutions'.
(a) 2x + 2y = 5
x - 4y = 0
(b) -x + y = 1
x + y = 2
(c) x - 3y + z = 1
x + y + 2z = 14
(d) -x - y = 1
-3x - 3y = 2
(e) 4y + z = 20
2x - 2y + z = 0
x + z = 5
x + y - z = 10
(f) 2x + z + w = 5
y - w = -1
3x - z - w = 0
4x + y + 2z + w = 9