Gleichungssystem - Beispiel
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2 🏠 + 1 🚁 + 4 🏍️ = 85 💎
3 🏠 + 1 🚁 + 1 🏍️ = 90 💎
1 🏠 + 2 🚁 + 5 🏍️ = 95 💎
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x 💎 = 🏠 : x = ?
y 💎 = 🚁 : y = ?
z 💎 = 🏍️ : z = ?
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1) 2 x + 1 y + 4 z = 85
2) 3 x + 1 y + 1 z = 90
3) 1 x + 2 y + 5 z = 95
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Rechnung 1:
3) 1 x + 2 y + 5 z = 95
-
2) 3 x + 1 y + 1 z = 90
-
1) 2 x + 1 y + 4 z = 85
_____________________
4) -4 x = -80
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Rechnung 2:
4) -4 x = -80 | : -4
x = 20 : 🏠 = 20 💎
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Rechnung 3:
1) 2 • 20 + 1 y + 4 z = 85 | - 2 • 20
5) 1 y + 4 z = 45
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Rechnung 4:
2) 3 • 20 + 1 y + 1 z = 90 | - 3 • 20
6) 1 y + 1 z = 30
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Rechnung 5:
5) 1 y + 4 z = 45
-
6) 1 y + 1 z = 30
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7) 3 z = 15
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Rechnung 6:
7) 3 z = 15 | : 3
z = 5 : 🏍️ = 5 💎
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Rechnung 7:
x = 20 💎, z = 5 💎
1) 2 x + 1 y + 4 z = 85
2 • 20 + 1 y + 4 • 5 = 85 | - 2•20 - 4•5
1 y = 25 : 🚁 = 25 💎
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Antwort:
x = 20: 🏠 = 20 💎
y = 25 : 🚁 = 25 💎
z = 5 : 🏍️ = 5 💎
