Dengan metode subsitusi tentukan himpunan penyelesaian fungsi berikut ini:

a.

6x + 3y = 1 …(1)

8x – 5y = -3 …(2)

Dari persamaan (1), diperoleh

6x + 3y = 1

3y = 1 – 6x

y = 1/3 – 2x

Substitusi y = 1/3 – 2x ke persamaan (2)

8x – 5(1/3 – 2x) = -3

8x – 5/3 + 10x = -3

18x = -3 + 5/3

18x = -9/3 + 5/3

18x = -4/3

x = -4/3 × 1/18

x = -2/3 × 1/9

x = -2/27

Substitusi x = -2/27 ke y = 1/3 – 2x

y = 1/3 – 2(-2/27)

y = 9/27 + 4/27

y = 13/27

HP = {(x, y)} = {(-2/27, 13/27)}

b.

8x – 5y = 9 …(1)

3x + 5y = 31 …(2)

Dari persamaan (1), diperoleh

8x – 5y = 9

8x – 9 = 5y

Substitusi 5y = 8x – 9 ke persamaan (2)

3x + (8x – 9) = 31

11x – 9 = 31

11x = 31 + 9

11x = 40

x = 40/11

Substitusi x = 40/11 ke 5y = 8x – 9

5y = 8(40/11) – 9

5y = 320/11 – 99/11

5y = 221/11

y = 221/11 × 1/5

y = 221/55

HP = {(x, y)} = {(40/11, 221/55)}

Semoga membantu.

Penjelasan dengan langkah-langkah:

a.

6x + 3y = 1……………(1)

8x – 5y + 3 = 0………(2)

5y = 8x + 3

y = 1/5(8x + 3)

subtitusikan y kepersamaan (1)

6x + 3y = 1

6x + 3[ 1/5(8x + 3)] = 1

6x + 24/5x + 9/5 = 1

30x + 24x + 9 = 5

54x = – 4

x = – 4/54

x = – 2/27

subtitusikan nilai x ke persamaan (1)

6x + 3y = 1

6(-4/54) + 3y = 1

3y = 1 + 24/54

3y = 54/54 + 24/54

y = (78/54)/3

y = 26/54

y = 13/27

HP = { -2/27, 13/27 }

b.

8x – 5y – 9 = 0……….(1)

3x + 5y – 31 = 0…….(2)

5y = – 3x + 31

subtitusikan 5y kepersamaan (1)

8x – 5y – 9 = 0

8x – (-3x + 31) – 9= 0

8x + 3x – 31 – 9 = 0

11x = 40

x = 40/11

subtitusikan nilai x kepersamaan (1)

8x – 5y – 9 = 0

8(40/11) – 5y – 9 = 0

320/11 – 5y – 9 = 0

5y = 320/11 – 9 = 0

5y = 320/11 – 99/11 = 0

5y = 221/11

y = 221/55

HP = {40/11, 221/55}