Question

resolva em sistema 3x3
2x−5y+3z=1
−5x+y−4z=15
7x−2y+5z=18​

Answer 1

Resposta:

y=(−49/3)

x=98/3

z=(−146/3)

Explicação passo a passo:

2x−5y+3z=1

−5x+y−4z=15

7x−2y+5z=18​

4(2x−5y+3z)=4(1)

8x−20y+12z=4

3(−5x+y−4z)=3(15)

−15x+3y−12z=45

8x−20y+12z+(−15x+3y−12z)=4+45

8x−20y+12z−15x+3y−12z=49

8x−20y−15x+3y=49

−7x−20y+3y=49

−7x−17y=49

7x+17y=(−49)

−5(2x−5y+3z)=(−5)(1)

−10x+25y−15z=(−5)

3(7x−2y+5z)=3(18​)

21x−6y+15z=54

21x−6y+15z+(−10x+25y−15z)=54+(−5)

21x−6y+15z−10x+25y−15z=54−5

21x−6y−10x+25y=49

11x−6y+25y=49

11x+19y=49

11x+19y+7x+17y=49−49

18x+19y+17y=0

18x+36y=0

18(x+2y)=0

x+2y=0/18

x+2y=0

11x+19y=49

11x=49−19y

11(x+2y)=11(0)

11x+22y=0

49−19y+22y=0

49+3y=0

3y=(−49)

y=(−49/3) ← Resposta y.

x+2y=0

x+2(−49/3)=0

x−98/3=0

x=0+98/3

x=(98/3) ← Resposta x.

2x−5y+3z=1

2(98/3)−5(−49/3)+3z=1

196/3+245/3+3z=1

196/3+245/3+3z(3/3)=1

196/3+245/3+9z/3=1

(196+245+9z)/3=1

196+245+9z=3

441+9z=3

9z=3−441

9z=(−438)

z=(−438/9)

z=((−438:3)/(9:3))

z=(−146/3) ← Resposta z.