Résoudre en utilisant la méthode de substitution : 5x - 2y = -7 3x + y = -2 6x + y = 8 10x + 7y = -8 7x + 4y = -5 x + 3y = 9

5x - 2y = -7
3x + y = -2

y = - 2 - 3x
5x - 2 (- 2 - 3x) = - 7
5x + 4 + 6x = - 7
11x = - 7 - 4
11x = - 11
x = - 11/11
x = - 1

3x + y = - 2
3 * - 1 + y = - 2
- 3 + y = - 2
y = - 2 + 3
y = 1
Les solutions sont : (- 1 ; 1)

6x + y = 8
10x + 7y = -8

6x + y = 8
y = 8 - 6x

10x + 7y = - 8
10x + 7 (8 - 6x) = - 8
10x + 56 - 42x = - 8
10x - 42x = - 8 - 56
- 32x = - 64
x = 64/32
x = 2

6x + y = 8
6 * 2 + y = 8
12 + y = 8
y = 8 - 12
y = - 4
Les solutions sont : (2 ; - 4)

7x + 4y = -5
x + 3y = 9

x + 3y = 9
x = 9 - 3y

7x + 4y = - 5
7 (9 - 3y) + 4y = - 5
63 - 21y + 4y = - 5
- 21y + 4y = - 5 - 63
- 17y = - 68
y = 68/17
y = 4

x + 3y = 9
x + 3 * 4 = 9
x + 12 = 9
x = 9 - 12
x = - 3
Les solutions sont : (- 3 ; 4)