{3х+4у+5z=22
{x-6y-6z=-9
{2x+4y-4z=10 |:2
{3x+4y+5z=22
{x= -9+6y+6z
{x+2y-2z=5
{3(-9+6y+6z) +4y+5z=22
{(- 9+6y+6z) +2y -2z=5
{-27 +18y+18z +4y +5z=22
{-9 +8y+4z=5
{22y + 23z= 22+27
{8y+4z=5+9 |:4
{22y +23z =49
{2y +z= 3.5
{22y+23z=49
{z=3.5-2y
22y +23(3.5-2y)=49
22y +80.5 - 46y=49
-24y= 49-80.5
-24y= -31.5
y= (-31.5) : (-24)
у= 1,3125
z= 3.5 - 2 *1.3125
z= 3.5- 2.625
z=0.875
x= -9 +6*1.3125 +6*0.875
x=-9 + 7.875+ 5.25
x= 13.125-9
x=4.125
проверим:
3*4,125 +4*1,3125+5*0,875= 12,375+5,25+4,375=22
4,125-6*1,3125 -6*0,875 = 4,125-7,875-5,25= -9
2*4,125 +4*1,3125 -4*0,875 = 8,25 +5,25 - 3,5 =10
Ответ: х=4,125 ; у= 1,3125 ; z=0, 875 .