| a) Auflösen: (1) 5x + y = 7 |-5x |
| (1') y = -5x + 7 |
| Einsetzen in (2): 2x + (-5x + 7) = 4 |
| -3x + 7 = 4 |-7 |
| -3x = -3 |:-3 |
| x = 1 |
| Einsetzen in (1'): y = -5 * (1) + 7 |
| y = 2 |
| |
| b) Auflösen: (1) x + 3y = 5 |-3y |
| (1') x = -3y + 5 |
| Einsetzen in (2): (-3y + 5) - 2y = 10 |
| -5y + 5 = 10 |-5 |
| -5y = 5 |:-5 |
| y = -1 |
| Einsetzen in (1'): x = -3(-1) + 5 |
| x = 3 + 5 |
| x = 8 |
| |
| c) 3x - 2y = 2 |+2y |
| 3x = 2y + 2 |-2 |
| 3x - 2 = 2y |
| Einsetzen: 5x + (3x - 2) = 14 |
| 8x - 2 = 14 |+2 |
| 8x = 16 |:8 |
| x = 2 |
| Einsetzen: 3(2) - 2 = 2y |
| 6 - 2 = 2y |
| 4 = 2y |:2 |
| y = 2 |
| |
| d) 4x + 3y = 15 |-3y |
| 4x = -3y + 15 |
| Einsetzen: (-3y + 15) - 2y = 10 |
| -5y + 15 = 10 |-15 |
| -5y = -5 |:-5 |
| y = 1 |
| Einsetzen: 4x = -3(1) + 15 |
| 4x = -3 + 15 |
| 4x = 12 |:4 |
| x = 3 |
| |
| e) 2x = 3y - 3 |+3 |
| 2x + 3 = 3y |
| Einsetzen: x - (2x + 3) = -9 |
| -x - 3 = -9 |+3 |
| -x = -6 |:-1 |
| x = 6 |
| Einsetzen: 2(6) + 3 = 3y |
| 12 + 3 = 3y |
| 15 = 3y |:3 |
| y = 5 |
| |
| f) 5x - 3y = 1 |+3y |
| 5x = 3y + 1 |-1 |
| 5x - 1 = 3y |
| Einsetzen: x + (5x - 1) = 11 |
| 6x - 1 = 11 |+1 |
| 6x = 12 |:6 |
| x = 2 |
| Einsetzen: 5(2) - 1 = 3y |
| 10 - 1 = 3y |
| 9 = 3y |:3 |
| y = 3 |
| |
| g) 4x - 2y = 16 |+2y |
| 4x = 2y + 16 |:4 |
| x = y/2 + 4 |
| Einsetzen: 4y = 5(y/2 + 4) - 7 |
| 4y = 5y/2 + 20 - 7 |
| 4y = 5y/2 + 13 |*2 |
| 8y = 5y + 26 |-5y |
| 3y = 26 |:3 |
| y = 26/3 |
| Einsetzen: x = (26/3)/2 + 4 |
| x = 13/3 + 4 |
| x = 25/3 |
| |
| h) 4x - 3y = 11 |+3y |
| 4x = 3y + 11 |:4 |
| x = 3y/4 + 11/4 |
| Einsetzen: 6y + 28 = 2(3y/4 + 11/4) |
| 6y + 28 = 3y/2 + 11/2 |*2 |
| 12y + 56 = 3y + 11 |-3y |
| 9y + 56 = 11 |-56 |
| 9y = -45 |:9 |
| y = -5 |
| Einsetzen: x = 3(-5)/4 + 11/4 |
| x = -15/4 + 11/4 |
| x = -4/4 |
| x = -1 |
|
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