SYSTEM OF LINEAR EQUATION THREE VARIABLE / SISTEM PERSAMAAN LINEAR TIGA VARIABEL

System of linear equation three variable Calculator
Kalkulator Sistem Persamaan Linear Tiga Variabel

Input constant and coefisien of x, y and z

Masukkan Koofisien x, y, z dan konstanta

x + y + z =
x + y + z =
x + y + z =

x =
y =
z =

For Example / Contoh:
Find a solution to the following system:
Carilah penyelesaian dari sistem persamaan berikut ini:
x + y + z = 6
2x + 3y - z = 5
3x - y + 2z = 7

Solution / Jawaban:
Solving by Elimination and Subtitution.
Penyelesainnya dengan cara eliminasi dan subtitusi [Campuran].

[1]  $x+y+z=6$
[2]  $2x+3y-z=5$
[3]  $3x-y+2z=7$

Eliminate z by adding equation [1] and [2]
Eliminasi z dengan menjumlahkan persamaan [1] dan [2]
$x+y+z=6$
$2x+3y-z=5$

--------------------------  +
$3x+4y=11$  [4]

2×[1] - [3]
$2x+2y+2z=12$
$3x-y+2z=7$
---------------------------  -
$-x+3y=5$  [5]

[4] + 3×[5]
$3x+4y=11$
$-3x+9y=15$
----------------------  +
$13y=26$
$y=\frac{26}{13}$
$y=2$

Use [5] to find x
$-x+3y=5$
$-x+3×2=5$
$-x+6=5$
$-x=5-6$
$-x=-1$
$x=1$

Use [1] to find z
$x+y+z=6$
$1+2+z=6$
$z=6-3$
$z=3$

The solution is x = 1, y = 2 and z = 3
Penyelesaiannya adalah x = 1, y = 2 dan z = 3

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