Résoudre par substitution [tex] \left \{ {{x+5y=12} \atop {4x-3y=2}} \right. [/tex]

bonjour

x + 5 y = 12
4 x - 3 y = 2

x = 12 - 5 y

4 ( 12 - 5 y) - 3 y = 2
48 - 20 y - 3 y = 2

- 23 y = 2 - 48
- 23 y = - 46

- y = - 2
y = 2

x + 10 = 12
x = 12 - 10
x = 2

x + 5y = 12
4x - 3y = 2

x + 5y = 12
x = 12 - 5y

4x - 3y = 2
4 (12 - 5y) - 3y = 2
48 - 20y - 3y = 2
48 - 23y = 2
- 23y = 2 - 48
y = 46/23
y = 2

x + 5y = 12
x + 5 (2) = 12
x + 10 = 12
x = 12 - 10
x = 2

Les solutions sont : (2 ; 2)