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y - 5 x = 30

$y - 5 x = 30$ ,

y > x + 2

$y > x + 2$

Langkah 1

Memasukkan variabel slack

u

$u$ dan

v

$v$ untuk menggantikan pertidaksamaan dengan persamaan.

y - Z = x + 2

$y - Z = x + 2$

y - 5 x - 30 = 0

$y - 5 x - 30 = 0$

Langkah 2

Kurangkan

x

$x$ dari kedua sisi persamaan tersebut.

y - Z - x = 2, y - 5 x - 30 = 0

$y - Z - x = 2, y - 5 x - 30 = 0$

Langkah 3

Tambahkan

30

$30$ ke kedua sisi persamaan.

y - Z - x = 2, y - 5 x = 30

$y - Z - x = 2, y - 5 x = 30$

Langkah 4

Tulis sistem persamaan tersebut dalam bentuk matriks.

[\begin{array}{c} - 1 & 1 & 0 & 2 \\ - 5 & 1 & 0 & 30 \end{array}]

$[\begin{array}{c} - 1 & 1 & 0 & 2 \\ - 5 & 1 & 0 & 30 \end{array}]$

Langkah 5

Tentukan bentuk eselon baris yang dikurangi.

Ketuk untuk lebih banyak langkah...

Langkah 5.1

Multiply each element of

R_{1}

$R_{1}$ by

- 1

$- 1$ to make the entry at

1, 1

$1, 1$ a

1

$1$ .

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Langkah 5.1.1

Multiply each element of

R_{1}

$R_{1}$ by

- 1

$- 1$ to make the entry at

1, 1

$1, 1$ a

1

$1$ .

[\begin{array}{c} - - 1 & - 1 \cdot 1 & - 0 & - 1 \cdot 2 \\ - 5 & 1 & 0 & 30 \end{array}]

$[\begin{array}{c} - - 1 & - 1 \cdot 1 & - 0 & - 1 \cdot 2 \\ - 5 & 1 & 0 & 30 \end{array}]$

Langkah 5.1.2

Sederhanakan

R_{1}

$R_{1}$ .

[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ - 5 & 1 & 0 & 30 \end{array}]

$[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ - 5 & 1 & 0 & 30 \end{array}]$

[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ - 5 & 1 & 0 & 30 \end{array}]

$[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ - 5 & 1 & 0 & 30 \end{array}]$

Langkah 5.2

Perform the row operation

R_{2} = R_{2} + 5 R_{1}

$R_{2} = R_{2} + 5 R_{1}$ to make the entry at

2, 1

$2, 1$ a

0

$0$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.2.1

Perform the row operation

R_{2} = R_{2} + 5 R_{1}

$R_{2} = R_{2} + 5 R_{1}$ to make the entry at

2, 1

$2, 1$ a

0

$0$ .

[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ - 5 + 5 \cdot 1 & 1 + 5 \cdot - 1 & 0 + 5 \cdot 0 & 30 + 5 \cdot - 2 \end{array}]

$[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ - 5 + 5 \cdot 1 & 1 + 5 \cdot - 1 & 0 + 5 \cdot 0 & 30 + 5 \cdot - 2 \end{array}]$

Langkah 5.2.2

Sederhanakan

R_{2}

$R_{2}$ .

[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ 0 & - 4 & 0 & 20 \end{array}]

$[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ 0 & - 4 & 0 & 20 \end{array}]$

[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ 0 & - 4 & 0 & 20 \end{array}]

$[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ 0 & - 4 & 0 & 20 \end{array}]$

Langkah 5.3

Multiply each element of

R_{2}

$R_{2}$ by

- \frac{1}{4}

$- \frac{1}{4}$ to make the entry at

2, 2

$2, 2$ a

1

$1$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.3.1

Multiply each element of

R_{2}

$R_{2}$ by

- \frac{1}{4}

$- \frac{1}{4}$ to make the entry at

2, 2

$2, 2$ a

1

$1$ .

[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ - \frac{1}{4} \cdot 0 & - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot 0 & - \frac{1}{4} \cdot 20 \end{array}]

$[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ - \frac{1}{4} \cdot 0 & - \frac{1}{4} \cdot - 4 & - \frac{1}{4} \cdot 0 & - \frac{1}{4} \cdot 20 \end{array}]$

Langkah 5.3.2

Sederhanakan

R_{2}

$R_{2}$ .

[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ 0 & 1 & 0 & - 5 \end{array}]

$[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ 0 & 1 & 0 & - 5 \end{array}]$

[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ 0 & 1 & 0 & - 5 \end{array}]

$[\begin{array}{c} 1 & - 1 & 0 & - 2 \\ 0 & 1 & 0 & - 5 \end{array}]$

Langkah 5.4

Perform the row operation

R_{1} = R_{1} + R_{2}

$R_{1} = R_{1} + R_{2}$ to make the entry at

1, 2

$1, 2$ a

0

$0$ .

Ketuk untuk lebih banyak langkah...

Langkah 5.4.1

Perform the row operation

R_{1} = R_{1} + R_{2}

$R_{1} = R_{1} + R_{2}$ to make the entry at

1, 2

$1, 2$ a

0

$0$ .

[\begin{array}{c} 1 + 0 & - 1 + 1 \cdot 1 & 0 + 0 & - 2 - 5 \\ 0 & 1 & 0 & - 5 \end{array}]

$[\begin{array}{c} 1 + 0 & - 1 + 1 \cdot 1 & 0 + 0 & - 2 - 5 \\ 0 & 1 & 0 & - 5 \end{array}]$

Langkah 5.4.2

Sederhanakan

R_{1}

$R_{1}$ .

[\begin{array}{c} 1 & 0 & 0 & - 7 \\ 0 & 1 & 0 & - 5 \end{array}]

$[\begin{array}{c} 1 & 0 & 0 & - 7 \\ 0 & 1 & 0 & - 5 \end{array}]$

[\begin{array}{c} 1 & 0 & 0 & - 7 \\ 0 & 1 & 0 & - 5 \end{array}]

$[\begin{array}{c} 1 & 0 & 0 & - 7 \\ 0 & 1 & 0 & - 5 \end{array}]$

[\begin{array}{c} 1 & 0 & 0 & - 7 \\ 0 & 1 & 0 & - 5 \end{array}]

$[\begin{array}{c} 1 & 0 & 0 & - 7 \\ 0 & 1 & 0 & - 5 \end{array}]$

Langkah 6

Gunakan matriks hasil untuk menyatakan penyelesaian akhir untuk sistem persamaan tersebut.

x = 0

$x = 0$

y = 0

$y = 0$

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