Sistem Persamaan Linear Dua Variabel

MathematicsLinear EquationsMedium

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Harga 2 buku tulis dan 3 pensil adalah Rp21.000,00. Sedangkan harga 3 buku tulis dan 1 pensil adalah Rp24.500,00. Berapakah harga 1 buku tulis dan 2 pensil?

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1
Step 1

Halo, mari kita selesaikan soal ini bersama-sama. Pertama, kita definisikan variabelnya terlebih dahulu.

Definisi Variabel

$$b = \text{harga 1 buku tulis}$$
$$p = \text{harga 1 pensil}$$
2
Step 2

Berdasarkan informasi, kita punya sistem persamaan linear dua variabel sebagai berikut.

$$2b + 3p = 21000$$
$$3b + p = 24500$$
3
Step 3

Mari kita gunakan metode substitusi. Dari persamaan kedua, kita dapat menyatakan p dalam b.

$$3b + p = 24500$$
$$p = 24500 - 3b$$
4
Step 4

Selanjutnya, kita masukkan nilai p ini ke dalam persamaan pertama.

$$2b + 3p = 21000$$
$$2b + 3(24500 - 3b) = 21000$$
5
Step 5

Mari kita hitung persamaan tersebut. Kalikan tiga ke dalam kurung.

$$2b + 73500 - 9b = 21000$$
6
Step 6

Gabungkan suku-suku yang mengandung b.

$$-7b + 73500 = 21000$$
7
Step 7

Kurangi kedua sisi dengan 73500.

$$-7b = 21000 - 73500$$

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About This Question

Subject
Mathematics
Topic
Linear Equations
Difficulty
Medium
Question Type
Open Ended

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