Following 2896

Solve the following set of equations with three unknowns.

3x + 2y + 3z = 110
5x-y-4z = 0
2x-3y + z = 0

Correct answer:

x =  13.75
y =  13.75
z =  13.75

Step-by-step explanation:


3x+2y+3z=110
5x-y-4z=0
2x-3y+z=0

3·x+2·y+3·z=110
5·x-y-4·z=0
2·x-3·y+z=0

3x+2y+3z = 110
5x-y-4z = 0
2x-3y+z = 0

Pivot: Row 1 ↔ Row 2
5x-y-4z = 0
3x+2y+3z = 110
2x-3y+z = 0

Row 2 - 3/5 · Row 1 → Row 2
5x-y-4z = 0
2.6y+5.4z = 110
2x-3y+z = 0

Row 3 - 2/5 · Row 1 → Row 3
5x-y-4z = 0
2.6y+5.4z = 110
-2.6y+2.6z = 0

Row 3 + Row 2 → Row 3
5x-y-4z = 0
2.6y+5.4z = 110
8z = 110


z = 110/8 = 13.75
y = 110-5.4z/2.6 = 110-5.4 · 13.75/2.6 = 13.75
x = 0+y+4z/5 = 0+13.75+4 · 13.75/5 = 13.75

x = 55/4 = 13.75
y = 55/4 = 13.75
z = 55/4 = 13.75

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