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| Klasse | | 8. Klasse |
| Schulbuch | | Schnittpunkt 8 Mathematik für Realschulen Baden-Württemberg |
| Seite | | Seite 133 - Einsetzungsverfahren |
| Aufgabe | |
4 vorherige Aufgabe • nächste Aufgabe |
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| Lösung | |
| a) 5x + y = 8 |
| 5x + 3x = 8 |
| 8x = 8 |
| x = 1 |
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| y = 3x |
| y = 3 * 1 |
| y = 3 |
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| b) 7x - y = -15 |
| 7x - 2x = -15 |
| 5x = -15 |
| x = -3 |
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| y = 2x |
| y = 2 * (-3) |
| y = -6 |
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| c) x + 2y = 49 |
| 5y + 2y = 49 |
| 7y = 49 |
| y = 7 |
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| x = 5y |
| x = 5 * 7 |
| x = 35 |
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| d) 2x - 3y = 7 |
| 5y - 3y = 7 |
| 2y = 7 |
| y = 7/2 |
| y = 3,5 |
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| 2x = 5y |
| 2x = 5 * (7/2) |
| 2x = 35/2 |
| 4x = 35 |
| x = 35/4 |
| x = 8,75 |
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| e) 3x + y = 11 |
| 3x + (x + 1) = 11 |
| 4x + 1 = 11 |
| 4x = 10 |
| x = 10/4 = 5/2 |
| x = 2,5 |
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| y = x + 1 |
| y = 5/2 + 1 = 7/2 |
| y = 3,5 |
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| f) 5x + y = 45 |
| 5x + (2x - 4) = 45 |
| 7x - 4 = 45 |
| 7x = 49 |
| x = 7 |
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| y = 2x - 4 |
| y = 2 * 7 - 4 = 14 - 4 |
| y = 10 |
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| g) x - 2y = 7 |
| (5y + 4) - 2y = 7 |
| 3y + 4 = 7 |
| 3y = 3 |
| y = 1 |
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| x = 5y + 4 |
| x = 5 * 1 + 4 = 5 + 4 |
| x = 9 |
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| h) 3y + x = 9 |
| 3y + (y - 5) = 9 |
| 4y - 5 = 9 |
| 4y = 14 |
| y = 14/4 = 7/2 |
| y = 3,5 |
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| x = y - 5 |
| x = 7/2 - 5 |
| x = 7/2 - 10/2 = - 3/2 |
| x = -1,5 |
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| i) 2x + 3y = 9 |
| (y + 1) + 3y = 9 |
| 4y + 1 = 9 |
| 4y = 8 |
| y = 2 |
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| 2x = y + 1 |
| 2x = 2 + 1 = 3 |
| x = 3/2 = 1,5 |
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| k) 3x + 5y = 17 |
| 3x + (6x - 1) = 17 |
| 9x - 1 = 17 |
| 9x = 18 |
| x = 2 |
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| 5y = 6x - 1 |
| 5y = 6 * 2 - 1 = 12 - 1 = 11 |
| y = 11/5 = 2,2 |
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