Tolong bantuin, 12. Diketahui sistem persamaan : x+y+ 2z = 6; x-y+z=-4; 2x + y - 2z = -4. Nilai xyz = ...

<p>Nilai xyz = <strong>-16</strong>.</p><p>&nbsp;</p><p><strong>Diketahui :</strong></p><p>x + y + 2z = 6 ... (1)</p><p>x - y + z = -4 ... (2)</p><p>2x + y - 2z = -4 ... (3)</p><p><strong>Ditanya : </strong>xyz = ... ?</p><p><strong>Dijawab :</strong></p><p>Pejumlahan persamaan (1) dan (2) untuk mengeliminasi nilai (y).</p><p>x + y + 2z = 6</p><p><u>x - &nbsp;y + &nbsp;z &nbsp;= -4</u> &nbsp;+</p><p>2x + 0 + 3z = 2</p><p>&nbsp; &nbsp; &nbsp; 2x + 3z = 2 ... (4)</p><p>Pengurangan persamaan (1) dan (3) untuk mengeliminasi nilai (y).</p><p>&nbsp;x &nbsp;+ y + 2z = 6</p><p><u>2x + y - 2z = -4</u> &nbsp;–</p><p>-x + 0 + 4z = 10</p><p>&nbsp; &nbsp; &nbsp; -x + 4z = 10 ... (5)</p><p>Penjumlahan persamaan (5) dan (4) untuk mengeliminasi nilai (x).</p><p>-x + 4z = 10 |2×| -2x + 8z = 20</p><p>2x + 3z = 2 &nbsp;|1×| &nbsp;<u>2x + 3z = 2 &nbsp;</u> &nbsp;+</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 0 + 11z = 22</p><p>z = ²²/₁₁→_&nbsp;<strong>z = 2</strong></p><p>Subtitusi z = 2 ke persamaan (4) untuk mencari nilai (x)</p><p>&nbsp; &nbsp;2x + 3z = 2</p><p>2x + 3(2) = 2</p><p>2x = 2 - 6</p><p>2x = -4</p><p>&nbsp; x = ^-4/₂ &nbsp;→ <strong>x = -2</strong></p><p>Substitusi x = -2 dan z = 2 ke persamaan (1) untuk mencari nilai (y)</p><p>&nbsp; &nbsp; x + y + 2z = 6</p><p>-2 + y + 2(2) = 6</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y + 2 = 6</p><p>y = 6 - 2 &nbsp;→ &nbsp;<strong>y = 4</strong></p><p>Maka nilai xyz adalah :</p><p>xyz = -2 × 4 × 2&nbsp;</p><p><strong>xyz = -16</strong></p><p>&nbsp;</p><p>Selesai :D🙏</p>