System Of Three-Variable Linier Equations

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System of Three-Variable Linier Equations




Andrea Fauzian

, SYSTEM OF LINEAR EQUATIONS

System of Three-Variable Linear Equations

a1x + b1 y + c1z = d1

1. General form: a 2 x + b 2 y + c 2 z = d 2
a x + b y + c z = d
 3 3 3 3

2. It can be solved by stratified and determinant methods of elimination.
3. Determinant method:

a1 b1 c1
= (a1b2c3 + b1c2a3 + c1a2b3) –
D = a2 b2 c2 =
(a3b2c1 + b3c2a1 + c3a2b1)
a3 b3 c3


d1 b1 c1 a1 d1 c1 a1 b1 d1
Dx = d 2 b2 c 2 ; Dy = a 2 d2 c 2 ; Dz = a 2 b2 d2 ;
d3 b3 c3 a3 d3 c3 a3 b3 d3

Dx Dy Dz
x= ; y= ; z=
D D D

QUESTION SETTLEMENT

1. Dina, Hesti, Winda, and Neni buy stationery at the
same store. Dina bought two notebooks, one pen Dina: 2𝑥 + 𝑦 + 𝑧 = 12.000 …………(1)
and one pencil, for Rp12,000.00. Hesti bought one Hesti: 𝑥 + 𝑦 + 𝑧 = 8.500 …………(2)
notebook, one pen and one pencil, for Rp8,500.00. Winda: 3𝑥 + 2𝑦 = 16.500 …………(3)
Winda bought three notebooks and two pens for Neni: 𝑥 + 2𝑧 = ⋯
Rp16,500.00. If Neni buys one notebook and two
pencils, she has to pay... From (1) and (2)
A. Rp6.500,00 2𝑥 + 𝑦 + 𝑧 = 12.000
B. Rp7.000,00 𝑥 + 𝑦 + 𝑧 = 8.500 _
C. Rp7.500,00 𝑥 = 3.500…………………(4)
D. Rp8.000,00
E. Rp9.500,00
From (3) and (4)
3𝑥 + 2𝑦 = 16.500
3(3.500) + 2𝑦 = 16.500
2𝑦 = 16.500 − 10.500 = 6.000
𝑦 = 3.000 ……………………….(5)