Three unknowns

A + B + C = 14
B - A - C = 4
2·A - B + C = 0

A+B+C = 14
A-B+C = -4
2A-B+C = 0

Pivot: Row 1 ↔ Row 3
2A-B+C = 0
A-B+C = -4
A+B+C = 14

Row 2 - 1/2 · Row 1 → Row 2
2A-B+C = 0
-0.5B+0.5C = -4
A+B+C = 14

Row 3 - 1/2 · Row 1 → Row 3
2A-B+C = 0
-0.5B+0.5C = -4
1.5B+0.5C = 14

Pivot: Row 2 ↔ Row 3
2A-B+C = 0
1.5B+0.5C = 14
-0.5B+0.5C = -4

Row 3 - -0.5/1.5 · Row 2 → Row 3
2A-B+C = 0
1.5B+0.5C = 14
0.667C = 0.667


C = 0.66666667/0.66666667 = 1
B = 14-0.5C/1.5 = 14-0.5 · 1/1.5 = 9
A = 0+B-C/2 = 0+9-1/2 = 4

A = 4
B = 9
C = 1

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