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Himpunan penyelesaian dari sistem persamaan linear tiga variabel ⎩⎨⎧​x+y−z=242x−y+2z=4x+2y−3z=36​ adalah {(x,y,z)}. Nilai x : y : z=....

Pertanyaan

Himpunan penyelesaian dari sistem persamaan linear tiga variabel

open curly brackets table attributes columnalign left end attributes row cell size 14px x size 14px plus size 14px y size 14px minus size 14px z size 14px equals size 14px 24 end cell row cell size 14px 2 size 14px x size 14px minus size 14px y size 14px plus size 14px 2 size 14px z size 14px equals size 14px 4 end cell row cell size 14px x size 14px plus size 14px 2 size 14px y size 14px minus size 14px 3 size 14px z size 14px equals size 14px 36 end cell end table close

adalah undefined. Nilai size 14px x size 14px space size 14px colon size 14px space size 14px y size 14px space size 14px colon size 14px space size 14px z size 14px equals....

  1. size 14px 2 size 14px space size 14px colon size 14px space size 14px 7 size 14px space size 14px colon size 14px space size 14px 1

  2. size 14px 2 size 14px space size 14px colon size 14px space size 14px 5 size 14px space size 14px colon size 14px space size 14px 4

  3. size 14px 2 size 14px space size 14px colon size 14px space size 14px 5 size 14px space size 14px colon size 14px space size 14px 1

  4. size 14px 1 size 14px space size 14px colon size 14px space size 14px 5 size 14px space size 14px colon size 14px space size 14px 2

  5. size 14px 1 size 14px space size 14px colon size 14px space size 14px 2 size 14px space size 14px colon size 14px space size 14px 5 size 14px space 

S. Dwi

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Diketahui

table row cell x plus y minus z equals 24 space space space space space space space space space space left parenthesis Persamaan space 1 right parenthesis end cell row cell 2 x minus y plus 2 z equals 4 space space space space space space space space space space space space left parenthesis Persamaan space 2 right parenthesis end cell row cell x plus 2 y minus 3 z equals 36 space space space space space space space space space space left parenthesis Persamaan space 3 right parenthesis end cell end table

Selanjutnya eliminasi persamaan 1 dan 2.

table row cell x plus y minus z equals 24 end cell row cell 2 x minus y plus 2 z equals space space 4 space space plus end cell row cell 3 x plus z equals 28 end cell end table

Kemudian eliminasi persamaan 2 dan 3.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell table row cell 2 x minus y plus 2 z equals 4 end cell cell cross times 2 end cell cell 4 x minus 2 y plus 4 z equals 8 end cell row cell x plus 2 y minus 3 z equals 36 end cell cell cross times 1 end cell cell x plus 2 y minus 3 z equals 36 end cell end table end cell end table

table attributes rowalign center baseline baseline end attributes row cell table attributes columnalign right center left columnspacing 0px end attributes row cell 4 x minus 2 y plus 4 z end cell equals cell space space 8 end cell end table end cell row cell table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 2 y minus 3 z end cell equals cell 36 space space plus end cell end table end cell row cell table attributes columnalign right center left columnspacing 0px end attributes row cell 5 x plus z end cell equals 44 end table end cell end table

Lalu eliminasi 3 x plus z equals 28 dan 5 x plus z equals 44.

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell table row cell 3 x plus z equals 28 end cell row cell 5 x plus z equals 44 space space space space space minus end cell row cell negative 2 x equals negative 16 end cell row cell x equals 8 end cell end table end cell end table

Substitusi x equals 8 ke persamaan 3 x plus z equals 28.

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x plus z end cell equals 28 row cell 3 left parenthesis 8 right parenthesis plus z end cell equals 28 row z equals 4 end table

Substitusi nilai x dan z ke persamaan 1.

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus y minus z end cell equals 24 row cell 8 plus y minus 4 end cell equals 24 row y equals cell 24 minus 8 plus 4 end cell row y equals 20 end table

Sehingga perbandingannya adalah

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x space space colon space space y space space colon space space z end cell row blank blank cell 8 space space colon space 20 space colon space space 4 end cell row blank blank cell 2 space space colon space space 5 space space colon space space 1 end cell end table   

Jadi, jawaban yang tepat adalah C.

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