Question

Resolva os sistemas lineares.
A)
x - y + z = 4
2x + y - z = 0
3x - y - 2z = 6


B)
2x - 3y - z = 4
x + 2y + z = 3
3x - y - 2z =1

Answer 1

A)
x - y + z = 4   (i)
2x + y - z = 0   (ii)
3x - y - 2z = 6   (iii)

(i)+(ii)

3x=4 ==>x=4/3

(ii)+(iii)

5x-3z=6  ==>20/3-3z=6 ==>20/3-6 =3z  ==>2/3=3z  ==>z=2/9

x - y + z = 4  ==>4/3-y+2/9=4 ==>12-9y+2=36 ==>9y=-22 ==>y=-22/9

Resposta ===> (x,y,z)=(4/3 , -22/9 , 2/9)

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B)
2x - 3y - z = 4  (i)
x + 2y + z = 3  (ii)
3x - y - 2z =1      ==>vezes 2 ==> 6x-2y-4z=2 (iii)

(i)+(ii)

3x-y=7  ==>y=3x-7

(ii)+(iii)

7x-3z=5   ==>z= (7x-5)/3

x + 2y + z = 3

x + 2*(3x-7) + (7x-5)/3 = 3

tudo vezes 3

3x +18x-42+7x-5=9

28x=56 ==>x=2

y=3x-7 =6-7=-1

z= (7x-5)/3 = (14-5)/3=3

Resposta  ===>(x,y,z)=(2,-1,3)