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Réponse :
Bonjour
Exercice 1
1) x - y = 4 ⇔ x = y + 4 ⇔ x = y + 4
2x + 5y = -6 2(y + 4) + 5y = -6 2y + 8 + 5y = -6
⇔ x = y + 4 ⇔ x = y + 4 ⇔ x = -2 + 4 ⇔ x = 2
7y = - 14 y = -2 y = -2 y = -2
2) 3a + b = 3 ⇔ b = 3 - 3a ⇔ b = 3 - 3a
5a + 2b = 3 5a + 2(3 - 3a) = 3 5a + 6 - 6a = 3
⇔ b = 3 - 3a ⇔ b = 3 - 3a ⇔ b = 3 - 3×3 ⇔ b = -6
-a = -3 a = 3 a = 3 a = 3
Exercice 2
1) -x + 10y = -1 ⇔ x = 10y + 1 ⇔ x = 10y + 1
2x + 5y = 8 2(10y + 1) + 5y = 8 20y + 2 + 5y = 8
⇔ x = 10y + 1 ⇔ x = 10y + 1 ⇔ x = 10×6/25 + 1 ⇔ x = 17/5
25y = 6 y = 6/25 y = 6/25 y = 6/25
2) 2a + 5b = -3 ⇔ 2a = -3 - 5b ⇔ a = -3/2 - 5b/2
5a + 2b = 3 5a + 2b = 3 5(-3/2 - 5b/2) + 2 b = 3
⇔ a = -3/2 - 5b/2 ⇔ a = -3/2 - 5b/2 ⇔ a = -3/2 - 5b/2
-15/2 - 25b/2 + 2b = 3 -21b/2 = 3 + 15/2 -21b/2 = 21/2
⇔ a = -3/2 - 5b/2 ⇔ a = -3/2 - 5b/2 ⇔ a = -3/2 - 5×(-1)/2
b = 21/2 ×(-2/21) b = -1 b = -1
⇔ a = 1
b = -1