Solve 28

x + 2y - z = -1
3x + 8y+ 2z = 28
4x + 9y + z =14

x + 2·y - z = -1
3·x + 8·y+ 2·z = 28
4·x + 9·y + z =14

x+2y-z = -1
3x+8y+2z = 28
4x+9y+z = 14

Pivot: Row 1 ↔ Row 3
4x+9y+z = 14
3x+8y+2z = 28
x+2y-z = -1

Row 2 - 3/4 · Row 1 → Row 2
4x+9y+z = 14
1.25y+1.25z = 17.5
x+2y-z = -1

Row 3 - 1/4 · Row 1 → Row 3
4x+9y+z = 14
1.25y+1.25z = 17.5
-0.25y-1.25z = -4.5

Row 3 - -0.25/1.25 · Row 2 → Row 3
4x+9y+z = 14
1.25y+1.25z = 17.5
-z = -1


z = -1/-1 = 1
y = 17.5-1.25z/1.25 = 17.5-1.25 · 1/1.25 = 13
x = 14-9y-z/4 = 14-9 · 13-1/4 = -26

x = -26
y = 13
z = 1

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