MATEMATIKA (SPLTV)bantuin ya secepatnya•jgn ngasal

MATEMATIKA (SPLTV)bantuin ya secepatnya•jgn ngasal

Jawaban:

Sistem Persamaan Linear 3 Variabel

Penjelasan dengan langkah-langkah:

x+3y-z=6

x+y-3z=-2

2x-y+2z=-5

x²-y²+z=…

x+3y-z=6

x+y-3z=-2 –

2y+2z=8

x+y-3z=-2

2x-y+2z=-5 +

2x+2y-6z=-2

2x-y+2z=-5 –

3y-8z=3

2y+2z=8

3y-8z=3

8y+8z=8

3y-8z=3 +

11y =11

y =11/11

y =1

3y-8z=3

3(1)+8z=3

3+8z=3

8z=3-3

8z=0

z=0/8

z=0

x+3y-z=6

x+3(1)-0=6

x+3=6

x=6-3

x=3

x=3 y=1 z=0

x²-y²+z=3²-1²+0=9-1+0=8

2. 1/x=a

1/y=b

1/z=c

3a-2b+c=5

a-5b+3c=2

2a+b+c=12

3a-2b+c=5

a-5b+3c=2

3a-2b+c=5

3a-15b+9c=6 –

13b-8c=-1

a-5b+3c=2

2a+b+c=12

2a-10b+6c=4

2a+ b+ c=12 –

-11b+5c =-8

13b-8c=-1

-11b+5c=-8

65b-40c=-5

-88b+40c=-64 +

-23b =-69

b =-69/-23

b =3

13b-8c=-1

13(3)-8c=-1

39-8c=-1

-8c=-1-39

-8c=-40

c=-40/-8

c=5

3a-2b+c=5

3(a)-2(3)+5=5

3a-6+5=5

3a-1=5

3a=5+1

3a=6

a=6/3

a=2

a=2 b=3 c=5

1/x=a 1/y=b 1/z=c

1/x=2 1/y=3 1/z=5

1=2x 1=3y 1=5z

1/2=x 1/3=y 1/5=z

3. 1/2p+1/3q-3/4r=-1

1/2a+1/3b-3/4c=-1

1/3p-2/3q-3/4r=1

1/3a-2/3b-3/4c=1

1/6p+1/3q-1/4r=-1

1/6a+1/3b-1/4c=-1

1/2a+1/3b-3/4c=-1 x 12

1/3a-2/3b-3/4c=1 x 12

6a+4b-9c=-12

4a-8b-9c=12 –

2a+12b =-24

1/3a-2/3b-3/4c=1 x 12

1/6a+1/3b-1/4c=-1 x 36

4a- 8b-9c= 12

6a+12b-9c=-36 –

-2a-20b = 48

2a+12b=-24

-2a-20b=48 +

-8b=24

b=24/-8

b=-3

2a+12b=24

2a+12(-3)=24

2a-36=24

2a=24+36

2a=60

a=60/2

a=30

6a+4b-9c=-12

6(30)+4(-3)-9c=-12

180-12-9c=-12

168-9c=-12

-9c=-12-168

-9c=-180

c=-180/-9

c=20

masing masing variabel

a=30 b=-3 c=20

maka

p=30 q=-3 z=20

Demikian

Semoga membantu dan bermanfaat!