| a) Gleichsetzen: 2b + 4 = b + 5 |-b |
| b + 4 = b + 5 |-4 |
| b = 1 |
| Einsetzen: a = 1 + 5 |
| a = 6 |
| |
| b) 21 + 6n = 3m |:3 |
| 7 + 2n = m |
| 12m - 36 = 6n |+36 |
| 12m = 6n + 36 |:12 |
| m = n/2 + 3 |
| Gleichsetzen: n/2 + 3 = 7 + 2n |-n/2 |
| 3 = 7 + 3/2 n |-7 |
| -4 = 3/2 n |:3/2 |
| -8/3 = n |
| Einsetzen: 7 + 2 (-8/3) = m |
| 7 - 16/3 = m |
| 21/3 - 16/3 = m |
| m = 5/3 |
| |
| c) Gleichsetzen: 5 + t = 2t + 1 |-t |
| 5 = t + 1 |-1 |
| t = 4 |
| Einsetzen: s = 5 + 4 |
| s = 9 |
| |
| d) (1) 5p + 5q = 10 |-5p |
| (1') 5q = -5p + 10 |
| (2) 3p + 5q = 14 |-3p |
| (2') 5q = -3p + 14 |
| Gleichsetzen von (1') und (2'): -5p + 10 = -3p + 14 |+3p |
| -2p + 10 = 14 |-10 |
| -2p = 4 |:-2 |
| p = -2 |
| Einsetzen in (1'): 5q = -5 (-2) + 10 |
| 5q = 10 + 10 |
| 5q = 20 |:5 |
| q = 4 |
| |
| e) 2a + 2b = 0 |-2a |
| 2b = -2a |*2 |
| 4b = -4a |
| Gleichsetzen: -4a = 5a - 27 |+4a |
| 0 = 9a - 27 |+27 |
| 27 = 9a |:9 |
| a = 3 |
| Einsetzen: 2 * 3 + 2b = 0 |
| 6 + 2b = 0 |-6 |
| 2b = -6 |:2 |
| b = -3 |
| |
| f) (1) 7z + 5p = 9 |-7z |
| 5p = -7z + 9 |*2 |
| (1') 10p = -14z + 18 |
| (2) 10p -5z = -20 |+5z |
| (2') 10p = 5z - 20 |
| Gleichsetzen von (1') und (2'): -14z + 18 = 5z - 20 |+14z |
| 18 = 19z - 20 |+20 |
| 38 = 19z |:19 |
| z = 2 |
| Einsetzen in (1'): 10p = -14 * 2 + 18 |
| 10p = -28 + 18 |
| 10p = -10 |:10 |
| p = -1 |
|
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