System Of Two-Variable Linier Equations

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System of Two-Variable Linier Equations




Andrea Fauzian

, SYSTEM OF LINEAR EQUATIONS


System of Two-Variable Linear Equations
a1x + b1y = c1
1. General form: 
a 2 x + b 2 y = c 2
2. Can be solved by graph, substitution, elimination, and determinant method.
3. Determinant method:

a1 b1
D= = a1b2 – a2b2;
a2 b2

c1 b1 a c1
Dx = ;Dy = 1 ;
c2 b2 a2 c2

Dx Dy
x= ; y=
D D


QUESTION SETTLEMENT

1. Mrs. Abdaya shopping at the supermarket Abdaya : 5𝑝 + 4𝑖 = 550.000 .......(1)
bought 5 kg of beef-flavored meatballs and 4 Rita : 4𝑝 + 5𝑖 = 530.000 ......(2)
kg of fish-flavored meatballs at a price of Emi : 2𝑝 + 3𝑖 = ⋯
Rp550,000.00. Simultaneously at the
supermarket, Mrs. Rita Zahara bought 4 kg of Form (1) and (2)
beef-flavored meatballs and 5 kg of fish- 5𝑝 + 4𝑖 = 550.000.
flavored meatballs at a price of Rp530,000.00. 4𝑝 + 5𝑖 = 530.000 +
At the same supermarket, Mrs. Emi bought 2 9𝑝 + 9𝑖 = 1.080.000 .
kg of beef-flavored meatballs and 3 kg of fish- 𝑝 + 𝑖 = 120.0005𝑝 + 5𝑖 = 600.000 ....(3)
flavored meatballs, the money Mrs. Emi had to 2𝑝 + 2𝑖 = 240.000 ....(4)
pay was...
A. Rp240.000,00 Form (3) and (1)
B. Rp280.000,00 5𝑝 + 5𝑖 = 600.000.
C. Rp285.000,00 5𝑝 + 4𝑖 = 530.000 _
D. Rp290.000,00 𝑖 = 70.000 ...........................................(5)
E. Rp310.000,00
Form (4) and (5) obtained
2𝑝 + 2𝑖 = 240.000.
𝑖 = 70.000 +
2𝑝 + 3𝑖 = 310.000

Answer: E