Bagian a

1. Metode Substitusi

x + y = 8 .... (1)

y - x = 2

y = 2 + x.... (2)

• Substitusi pers (2) ke pers (1)

y + x = 8

2 + x + x = 8

2 + 2x = 8

2x = 8 - 2

2x = 6

x = 6/2

x = 3

• Substitusi nilai x ke pers (2)

y = 2 + x

y = 2 + 3

y = 5

Hp = {3, 5}

2. Metode Eliminasi

x + y = 8 .... (1)

y - x = 2

-x + y = 2 .... (2)

• Eliminasi x dari pers (1) dan (2)

x + y = 8

-x + y = 2

_______ +

2y = 10

y = 10/2

y = 5

• Eliminasi y dari pers (1) dan (2)

x + y = 8

-x + y = 2

_______ –

2x = 6

x = 6/2

x = 3

Hp = {3, 5}

3. Metode Grafik

x + y = 8

• Titik potong sumbu x (y = 0)

x + y = 8

x + 0 = 8

x = 8 → tipot = (8, 0)

• Titik potong sumbu y (x = 0)

x + y = 8

0 + y = 8

y = 8 → tipot = (0, 8)

-x + y = 2

• Titik potong sumbu x (y = 0)

-x + y = 2

-x + 0 = 2

x = -2 → tipot = (-2, 0)

• Titik potong sumbu y (x = 0)

-x + y = 2

0 + y = 2

y = 2 → tipot = (0, 2)

Gambar terlampir di slide 1

Bagian b

1. Metode Substitusi

x - 2y = -1

x = 2y - 1 ....(1)

2x + 3y = 12 .... (2)

• Substitusi pers (1) ke pers (2)

2x + 3y = 12

2(2y - 1) + 3y = 12

4y - 2 + 3y = 12

4y + 3y = 12 + 2

7y = 14

y = 14/7

y = 2

• Substitusi nilai y ke pers (1)

x = 2y - 1

x = 2(2) - 1

x = 4 - 1

x = 3

Hp = {3, 2}

2. Metode Eliminasi

• Eliminasi x dari pers (1) dan (2)

x - 2y = -1 | ×2| 2x - 4y = -2

2x + 3y = 12 | ×1| 2x + 3y = 12

__________ –

-7y = -14

y = 2

• Eliminasi y dari pers (1) dan (2)

x - 2y = -1 | ×3| 3x - 6y = -3

2x + 3y = 12 | ×2| 4x + 6y = 24

__________ +

7x = 21

x = 3

Hp = {3, 2}

3. Metode Grafik

x - 2y = -1

• Titik potong sumbu x (y = 0)

x - 2y = -1

x - 2(0) = -1

x - 0 = -1

x = -1 → tipot = (-1, 0)

• Titik potong sumbu y (x = 0)

x - 2y = -1

0 - 2y = -1

y = ½

y = 0,5 → tipot = (0; 0,5)

2x + 3y = 12

• Titik potong sumbu x (y = 0)

2x + 3y = 12

2x + 3(0) = 12

2x = 12

x = 6 → tipot = (6, 0)

• Titik potong sumbu y (x = 0)

2x + 3y = 12

2(0) + 3y = 12

3y = 12

y = 4 → tipot = (0, 4)

Gambar grafik terlampir pada slide kedua

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