Tentukan himpunan penyelesaian dari sistem persamaan linear tiga variabel berikut! 3x-2y + z = 12 2x + 3y + 5z = 8 x+y-3z = -1

<p>HP = {(x, y, z)} = <strong>{(3, -1, 1)}</strong></p><p>&nbsp;</p><p><strong>Diketahui :</strong></p><p>&nbsp; &nbsp;3x - 2y + z = 12 ... (1)</p><p>2x + 3y + 5z = 8 &nbsp; ... (2)</p><p>&nbsp; &nbsp; &nbsp;x + y - 3z = -1 &nbsp;... (3)</p><p><strong>Ditanya :</strong> HP = ... ?</p><p><strong>Dijawab :</strong></p><p>Menjumlahkan persamaan (1) dan (3) untuk eliminasi nilai y :</p><p>3x - 2y + z = 12 |1×| &nbsp; 3x - 2y + z = 12</p><p>&nbsp; x + y - 3z = -1 &nbsp;|2×| <u>2x + 2y - 6z = -2 &nbsp;</u> +</p><p>ㅤㅤㅤㅤㅤㅤㅤㅤㅤ &nbsp;5x + 0 - 5z = 10</p><p>5x - 5z = 10</p><p>&nbsp; &nbsp; x - z = 2</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;x = 2 + z ... (4)</p><p>Mengurangi persamaan (2) dan (3) untuk eliminasi nilai y :</p><p>2x + 3y + 5z = 8 |1×| 2x + 3y + 5z = 8&nbsp;</p><p>&nbsp; &nbsp; &nbsp;x + y - 3z = -1 |3×| <u>3x + 3y - 9z = -3</u> &nbsp;–</p><p>ㅤㅤㅤㅤㅤㅤㅤㅤㅤ &nbsp; -x + 0 + 14z = 11</p><p>-x + 14z = 11 ... (5)</p><p>Subtitusi x = 10 + z ke persamaan (5) untuk mencari nilai z :</p><p>-x + 14z = 11&nbsp;</p><p>-(2 + z) + 14z = 11</p><p>&nbsp; &nbsp; -2 - z + 14z = 11</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;13z = 11 + 2</p><p>13z = 13</p><p>&nbsp; &nbsp; z = ¹³/₁₃</p><p>&nbsp; &nbsp;<strong> z = 1</strong></p><p>Subtitusi z = 1 ke persamaan (4) untuk mencari nilai x :</p><p>x = 2 + z&nbsp;</p><p>x = 2 + 1</p><p><strong>x = 3</strong></p><p>Subtitusi x = 3 dan z = 1 ke persamaan (3) untuk mencari nilai y :</p><p>x + y - 3z = -1</p><p>3 + y - 3(1) = -1</p><p>&nbsp; &nbsp; &nbsp;3 + y - 3 = -1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 0 + y = -1</p><p><strong>y = -1</strong></p><p>&nbsp;</p><p>Selesai :D 🙏</p>