Pour chaque système, discuter de l'existence de solution. a/ 9x-6y=1 -8x+6y=-3 b / -10x+9y=10 10x+3y=-8

a/ 9x-6y=1                       
   -8x+6y=-3   

9x = 6y +1
x = 6/9y +1/9
x = 2/3y +1/9

-8x +6y =3
-8 ( 2/3y +1/9) +6y = 3
-16/3y -8/9 +6y = 3
-16/3y +18/3y = 3 +8/9
2/3 y = 27/9+8/9
2/3 y = 35/9
y = 35/9 * 3/2
y =  35/6

si y = 35/6
alors x = 2/3y +1/9
x = 2/3 *35/6 +1/9
x = 35/9 +1/9
x =36/9
x = 4


b/ -10x+9y=10
   10x+3y=-8

10x+3y = 8
10x = -3y +8
x = -3/10y +8/10
x = -3/10y +4/5

-10 (-3/10y +4/5) + 9y =10
3y +40/5 +9y =10
12y +8 =10
12y =10-8
12y =2
y =2/12
y =1/6

x = -3/10y +4/5
x = -3/10*1/6 +4/5
x =-3/60 +4/5
x = -1 /20 +4/5
x = -1/20 +16/20
x = 15/20
x = 3/4