Exercice 2 :
J'utilise la méthode par combinaison :
1) 5x - 6y = 9
- 4x + 3y = - 7
5x * 3 - 6y * 3 = 9 * 3
- 4x * 6 + 3y * 6 = - 7 * 6
15x - 18y = 27
- 24x + 18y = - 42
15x - 24x - 18y + 18y = 27 - 42
- 9x = - 15
x = - 15 / (- 9)
x = 5/3
x = 5/3
5 * 5/3 - 6y = 9
x = 5/3
25/3 - 6y = 9
x = 5/3
- 6y = 9 - 25/3
x = 5/3
- 6y = 2/3
x = 5/3
y = 2/3 : (- 6)
x = 5/3
y = - 1/9
Le couple solution est (5/3 ; - 1/9).
2) - 7x + 2y = 20
- x + 5y = - 25
- 7x * 5 + 2y * 5 = 20 * 5
- x * (- 2) + 5y * (- 2) = - 25 * (- 2)
- 35x + 10y = 100
2x - 10y = 50
- 35x + 2x + 10y - 10y = 100 + 50
- 33x = 150
x = - 150/33
x = - 50/11
x = - 50/11
- 7 * (- 50/11) + 2y = 20
x = - 50/11
350/11 + 2y = 20
x = - 50/11
2y = 20 - 350/11
x = - 50/11
2y = - 130/11
x = - 50/11
y = - 130/11 : 2
x = - 50/11
y = - 65/11
Le couple solution est (- 50/11 ; - 65/11).
