Résoudre ces deux système par substitution: A) -2x + y = -8 2x + 3y = 0 B) 2x + 7y = -13 x - 2y = 10

A)
-2x + y = -8
2x + 3y = 0

- 2x + y = - 8
y = - 8 + 2x
2x + 3y = 0
2x + 3 (- 8 + 2x) = 0
2x - 24 - 6x = 0
2x - 6x = 24
- 4x = 24
x = 24/4
x = 6

- 2x + y = - 8
- 2 * 6 + y = - 8
- 12 + y = - 8
y = - 8 + 12
y = 4

Les solutions sont : (6 ; 4)


B)
2x + 7y = -13
x - 2y = 10

x - 2y = 10
x = 10 + 2y

2x + 7y = - 13
2 (10 + 2y) + 7y = - 13
20 + 4y + 7y = - 13
20 + 11y = - 13
11y = - 13 - 20
11y = - 33
y = - 33/11
y = - 3

x - 2y = 10
x - 2 (- 3) = 10
x + 6 = 10
x = 10 - 6
x = 4

Les solutions sont : (4 ; - 3)

Résolution par la méthode de substitution
-2x + y = -8
2x + 3y = 0
- 2x + y = - 8
y = - 8 + 2x
2x + 3y = 0
2x + 3 (- 8 + 2x) = 0
2x - 24 - 6x = 0
2x - 6x = 24
- 4x = 24
x = 24/4
x = 6

- 2x + y = - 8
- 2 X 6 + y = - 8
- 12 + y = - 8
y = - 8 + 12
y = 4
Les solutions sont 6 et 4
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2x + 7y = -13
x - 2y = 10 
x - 2y = 10
x = 10 + 2y
2x + 7y = - 13
2(10 + 2y) + 7y = -13
20 + 4y + 7y = -13
20 + 11y = - 13
11y = - 13 - 20
11y = - 33
y = - 33/11
y = - 3

x - 2y = 10
x - 2 (- 3) = 10
x + 6 = 10
x = 10 - 6
x = 4

Les solutions sont : 4 et -3