Question

Rezolvati in R sistemul de ecuatii
$\left \{ {{x+y+z=1} \atop {2x-3y+2z=3}} \atop {3x-2y+z=4}\right.$

Answer 1

x+y+z=1
2x-3y+2z=3
3x-2y+z=4     
scadem din a 3-a  pe  prima
3x-2y+z-x-y-z=4-1
2x-3y=3   
2x-3y+2z=3
3+2z=3   ⇒ z=0  
x+y=1  x=1-y
2x-3y=3
2(1-y)-3y=3
2-2y-3y=3
5y=-1
y=-1/5
x=1-y=1-(-1/5)=1+1/5=6/5


verificare
x+y+z=1          6/5-1/5+0=5/5=1
2x-3y+2z=3    2*6/5+3*1/5+0=12/5+3/5=15/5=3
3x-2y+z=4      3*6/5+2*1/5+0=18/5+2/5=20/5=4