Question

Sistemas socorro?
A- -x+z=-3
3x+11y+2z=11
2x+3y+z=8
B- x+y+z=207
-x+y= 15
-y+z= 12
C- y+z=50
x+y=45
x+z=35
D- 3x-y+z= 0
X-2y+5z= 0
-x+y-2z=0

Answer 1

Olá Lee
A-) -x+z=-3
3x+11y+2z=11
2x+3y+z=8
-x=-3-z => x=3+z
3.(3+z)+11y+2z=11
9+3z+11y+2z=11
9+5z+11y=11
5z+11y=2
.......................
2.(3+z)+3y+z=8
6+2z+3y+z=8
6+3z+3y=8 => 3z+3y=2
5z+11y=2 . (3)
3z+3y=2 . (-11)
15z+33y=6
-33z-33y=-22
-----------------------
-18z=-16
z=16/18
z=8/9 <<<<<<
x=3+z => x=3+8/9 => x=(27+8)/9 => x=35/9 <<<<<
3.(8/9)+3y=2
24/9+3y=2
3y=2-24/9
3y=(18-24)/9
3y=-6/9
3y=-2/3
9y/3=-2/3
9y=-2
y=-2/9 <<<<
S={(35/9,-2/9,8/9)}
=====================
B- x+y+z=207 
-x+y= 15 
-y+z= 12 
y=15+x
-y=12-z => y=-12+z => y=z-12
z-12=15+x
z-x=27
-x+z=27 => x-z=-27 => x=-27+z
-27+z+y+z=207
-27+2z+y=207
y+2z=234
-y+z=12 . (-2)
y+2z=234
2y-2y=-24
------------------
3y=210 ==> y=70 <<<
y+2z=234 => 70+2z=234 => 2z=164 => z=82 <<<
x=-27+z => x=-27+82 => x=55 <<<
S={(55,70,82)}
===================
C-)
y+z=50
x+y=45
x+z=35
y=50-z
y=45-x
50-z=45-x
-z+x=45-50 => x-z=-5
x+z=35
x-z=-5
-------------
2x=30 => x=15
x+z=35 => 15+z=35 => z=20
y=50-z => y=50-20 => y=30
S={(15,30,20)}
====================
D-)
3x-y+z=0
x-2y+5z=0
-x+y-2z=0 => x-y+2z=0

3x-y+z=0 (i)
x-2y+5z=0 (ii)
x-y+2z=0 (iii)
..............
(ii)-(i)
x-2y+5z=0
3x-y+z=0 . (2)
x-2y+5z=0
6x-2y+2z=0
--------------------
-5x+3z=0 => 5x-3z=0
...................
(iii)-(i)
x-y+2z=0
3x-y+z=0
----------------
-2x+z=0 => 2x-z=0
5x-3z=0
2x-z=0 . (-3)
5x-3z=0
-6x+3z=0
------------------
-x=0 => x=0
5.0-3z=0 => -3z=0 => z=0
0-2y+0=0
-2y=0 => y=0
S={(0,0,0)} (solução trivial)