Question

Resolva o sistema
x+2y+z=8
2x-y+z=3
3x-2y+Z=2​

Answer 1

Resposta:

S={( 1 ; 2 ; 3)}

Explicação passo-a-passo:

x+2y+z=8

2x-y+z=3

3x-2y+Z=2

Método de Cramer :

(1 2 1)(1 2)

(2 -1 1)(2 -1)

(3 -2 1)(3 -2)

D=-1+6-4-(-3-2+4)

D=5-4-(-5+4)

D=1-(-1)

D=1+1

D=2

(8 2 1)(8 2)

(3 -1 1)(3 -1)

(2 -2 1)(2 -2)

DX=-8+4-6-(-2-16+6)

DX=-4-6-(-18+6)

DX=-10-(-12)

DX=-10+12

DX=2

(1 8 1)(1 8)

(2 3 1)(2 3)

(3 2 1)(3 2)

Dy=3 +24+4-(+9+2+16)

Dy=27+4-(11+16)

Dy=31-(27)

Dy= 31-27

Dy= 4

(1 2 8)(1 2)

(2 -1 3)(2 -1)

(3 -2 2)(3 -2)

Dz=-2+18-32-(-24-6+8)

Dz=16-32-(-30+8)

Dz=-16-(-22)

Dz=-16+22

Dz=6

Encontrando os valores das incógnitas:

x , y e z

X=DX/D=2/2= 1

Y=Dy/D=4/2= 2

Z=Dz/D=6/2= 3

Fazendo a verificação :

x+2y+z=8

1+2.(2)+3=8

1+4+3=8

1+7=8

8=8

ok!

2x-y+z=3

2.(1)-2+3=3

2-2+3=3

0+3=3

3=3

ok!

3x-2y+Z=2

3.(1)-2.(2)+3=2

3-4+3=2

-1+3=2

2=2

ok!