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

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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 💎