1. 2x + 3y = -1 dan 4x + 3y =7

( cara eliminasi )

2. 2x + 3y -8 = 0 dan 3x + 2y
-7 = 0 ( cara subsitusi )

3. 3x + 4y -20 =0 dan 5x = 6y –
7 ( cara campuran )

1. 2x + 3y = -1 dan 4x + 3y =7

Metode:

Nomor ❶ » Eleminasi
Nomor ❷ » Substitusi
Nomor ❸ » Campuran

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$LARGE{bf NOMOR : 1}$

$boxed{pink{sf Mencari : nilai : x}}$

2x + 3y = -1┃× 1┃

4x + 3y = 7┃× 1┃

↧↧↧↧↧↧↧↧↧↧↧↧↧↧↧↧

2x + 3y = -1

4x + 3y = 7ㅤ –

ㅤㅤ -2x = -8

ㅤㅤㅤ x = -8 : (-2)

ㅤㅤㅤ x = 4 ☑

$boxed{pink{sf Mencari : nilai : y}}$

2x + 3y = -1┃× 4┃

4x + 3y = 7┃× 2┃

↧↧↧↧↧↧↧↧↧↧↧↧↧↧↧↧

8x + 12y = -4

8x + ◌6y = 14ㅤ –

ㅤㅤㅤ6y = -18

ㅤㅤㅤ y = -18 : 6

ㅤㅤㅤ y = –3 ☑

$boxed{blue{sf HP : (x, y) = (4, -3)}}$

ㅤ

$LARGE{bf NOMOR : 2}$

» $sf 2x + 3y - 8 = 0$

$green{sf y = -dfrac{2}{3}x + dfrac{8}{3}}$ …… Pers. (i)

» $sf 3x + 2y - 7 = 0$

$green{sf 3x + 2y = 7}$ …… Pers. (ii)

$boxed{pink{sf Mencari : nilai : x}}$

Substitusikan pers. (i) ke pers. (ii)

$begin{aligned} sf 3x + 2y &= sf 7 \ sf 3x + 2(-frac{2}{3}x + frac{8}{3}) &= sf 7 \ sf 3x - frac{4}{3}x + frac{16}{3} &= sf 7 \ sf frac{9}{3}x - frac{4}{3}x &= sf 7 - frac{16}{3} \ sf frac{5}{3}x &= sf frac{21}{3} - frac{16}{3} \ sf frac{5}{3}x &= sf frac{5}{3} \ sf x &= sf frac{5}{3} : frac{5}{3} \ sf x &= boxed{sf 1} end{aligned}$

$boxed{pink{sf Mencari : nilai : y}}$

Substitusikan y = 1 ke dalam salah satu persamaan

$begin{aligned} sf y &= sf -frac{2}{3}x + frac{8}{3} \ sf y &= sf (-frac{2}{3} times 1) + frac{8}{3} \ sf y &= sf -frac{2}{3} + frac{8}{3} \ sf y &= sf dfrac{6}{3} \ sf y &= boxed{sf 2} end{aligned}$

$boxed{blue{sf HP : (x, y) = (1, 2)}}$

ㅤ

$LARGE{bf NOMOR : 3}$

» $sf 3x + 4y - 20$

$green{sf 3x + 4y = 20}$ …… Pers. (i)

» $sf 5x = 6y - 7$

$green{sf 5x - 6y = -7}$ …… Pers. (ii)

$boxed{pink{sf Mencari : nilai : x}}$

Mencari nilai x dengan metode Eleminasi

3x + 4y = 20 ┃× 6┃

5x – 6y = -7 ┃× 4┃

↧↧↧↧↧↧↧↧↧↧↧↧↧↧↧↧↧

18x + 24y = 120

20x – 24y = -28ㅤ –

ㅤㅤㅤ -2x = 148

ㅤㅤㅤㅤ x = 148 : (–2)

ㅤㅤㅤㅤ x = –74 ☑

$boxed{pink{sf Mencari : nilai : y}}$

Substitusikan x = –74 ke dalam salah satu persamaan

$begin{aligned} sf 3x + 4y &= sf 20 \ sf 3(-74) + 4y &= sf 20 \ sf -222 + 4y &= sf 20 \ sf 4y &= sf 20 + 222 \ sf 4y &= sf 242 \ sf y &= sf 242 : 4 \ sf y &= boxed{sf frac{121}{2}} end{aligned}$

$boxed{blue{sf HP : (x, y) = (-74, dfrac{121}{2})}}$

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PELAJARI LEBIH LANJUT

DETAIL JAWABAN

༘ Mapel: Matematika

༘ Kode soal: 02

༘ Kelas: VIII

༘ Materi: SPLDV

༘ Kategorisasi: 08.02.05

༘ Kata Kunci: Mencari HP dengan metode Eleminasi, Subsitusi, dan Campuran