Exercice1.
a) et b) coef.dir AB: 3/-12 = -1/4 => AB: y = -1/4x + b et contient (-3;5) => 5 = 3/4 + b => b = 17/4
AB = y = -1/4x + 17/4
c) y = 7/2x + b et (2;0) est sur la droite => 0 = 777 + b => b = -7
y = 7/2x - 7
d) intersection
y = -1/4x + 17/4
=>-1/4x + 17/4 = 7/2x - 7 => -15/4x = -45/4 => x = 3 => y = 7/2
y = 7/2x - 7
(3;7/2)
exercice2
D1 : y = 14 ; D2: x = -4
D3: y = ax et contient (1;-2) => -2 = a => D3: y = -2x
D4: coef.dir 1 et contient (0;12) => y = x + 12
D5: coef dir 6/2 = 3 et contient (0;6) => y = 3x + 6
D6: coef.dir 2/4 = 1/2 et contient (0,4) => y = 1/2x + 4
exercice 3
a) y = -2x + 4 => y = -10 + 4 = -6 => (5 ; -6)
x = 5
b) 3x + 2y = 11 fois 1
2x + y = 1 fois -2
-x = -1 => x = 1 => y = 1 - 2 = -1 => (1;-1)
c) y = x² - 6x + 4
=> x² - 6x = - 2x => x² - 4x = 0 => x(x-4) = 0 => x = 0 ou x = 4
y = -2x + 4
si x = 0 => y = 4 et si x = 4 => y = -4
(0;4) et (4;-4)
exercice 4
3x + 5y = 11 fois -2 -6x - 10y = -22
2x + 3 y = -6 fois 3 6x + 9y = -18 => somme -y = -40 => y = 40
3x + 5y = 11 fois -3 -9x - 15y = -33
2x + 3 y = -6 fois 5 10x + 15y = -30 => somme x = - 63
(-63;40)
