Himpunan penyelesaian sistem persamaan adalah berikut. Tentukan nilai a×b×c??

<p>a × b × c = <strong>-36 (E)</strong></p><p>&nbsp;</p><p><strong>Diketahui :</strong></p><p>x + y + z = 5 &nbsp; &nbsp; &nbsp; &nbsp;... (1)</p><p>2x - 3y -4z = -11 ... (2)</p><p>3x + 2y - z = - 6 &nbsp; ... (3)</p><p>x = a, y = b, dan z = c</p><p><strong>Ditanya : </strong>a × b × c = ... ?</p><p><strong>Dijawab :</strong></p><p>Penjumlahan persamaan (1) dan (3) untuk eliminasi nilai z :&nbsp;</p><p>&nbsp; &nbsp; x + y + z = 5 &nbsp; &nbsp;</p><p><u>&nbsp;3x + 2y - z = -6</u> &nbsp;+</p><p>4x + 3y + 0 = -1</p><p>&nbsp; &nbsp; &nbsp; 4x + 3y = -1 ... (4)</p><p>Pengurangan persamaan (2) dan (3) untuk eliminasi nilai z :</p><p>2x - 3y -4z = -11 |1×| &nbsp; &nbsp; 2x - 3y - 4z = -11</p><p>3x + 2y - z = -6 &nbsp; |4×| <u>12x + 8 y - 4z = -24 &nbsp;</u> –</p><p>ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ-10x - 11y + 0 = 13</p><p>10x + 11y = -13 ... (5)</p><p>Pengurangan persamaan (4) dan (5) untuk eliminasi nilai x :</p><p>&nbsp; &nbsp; 4x + 3y = -1 &nbsp; &nbsp;|5×| 20x + 15y = -5</p><p>10x + 11y = -13 |2×| <u>20x + 22y = -26&nbsp;</u> –</p><p>ㅤㅤㅤㅤㅤㅤㅤㅤㅤ &nbsp; &nbsp; &nbsp; &nbsp; 0 - 7y = 21</p><p>7y = -21</p><p>&nbsp;<strong> y = -3</strong></p><p>Subtitusi y = -3 ke persamaan (4) untuk mencari nilai x :</p><p>&nbsp; &nbsp; 4x + 3y = -1</p><p>4x + 3(-3) = -1</p><p>&nbsp; &nbsp; &nbsp; &nbsp;4x - 9 = -1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 4x = -1 + 9</p><p>4x = 8</p><p>&nbsp; <strong>x = 2</strong></p><p>Subtitusi x = 2 dan y = -3 ke persamaan (1) untuk mencari nilai z :</p><p>x + y + z = 5</p><p>2 - 3 + z = 5</p><p>&nbsp; &nbsp; -1 + z = 5</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; z = 5 + 1</p><p>&nbsp; &nbsp; &nbsp;<strong> &nbsp; &nbsp; &nbsp; z = 6</strong></p><p>Jika x = a, y = b, dan z = c, maka a × b × c adalah :</p><p>a × b × c = x × y × x</p><p>a × b × c = 2 × (-3) × 6</p><p>a × b × c = -36</p><p>&nbsp;</p><p>Selesai :D🙏</p>