yang bener ya 1. Selesaikan sistem persamaan linear tiga variabel berikut! x + 2y + 3z = 2 2x - y + z = 4 3x - y - z = 9

<p>Jawabnan yang tepat adalah</p><p>x = 23/7, &nbsp;y = 12/7 dan z = -6/7<br>&nbsp;</p><p>Pembahasan :</p><p>x + 2y + 3z = 2 &nbsp; &nbsp; (1)</p><p>2x - y + z = 4 &nbsp; &nbsp; &nbsp; &nbsp; (2)</p><p>3x - y - z = 9 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(3)</p><p>&nbsp;</p><p>Eliminasi z dari persamaan (2) dan (3)</p><p>2x - y + z = 4&nbsp;</p><p><u>3x - y - z = 9 &nbsp;</u> +</p><p>5x - 2y = 13 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (4)</p><p>&nbsp;</p><p>Eliminasi y dari persamaan (1) dan (2)</p><p>x + 2y + 3z = 2 &nbsp;|kali 1| --&gt; x + 2y + 3z = 2</p><p>2x - y + z = 4 &nbsp; &nbsp; |kali 2| --&gt; <u>4x -2y + 2z = 8&nbsp;</u> +</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;5x &nbsp; + 5y &nbsp;= 10</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;5(x + y) = 10</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;x + y = 5 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y = 5 - x &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (5)</p><p>Sunstitusikan persamaan (5) ke persamaan (4)</p><p>5x - 2y = 13&nbsp;</p><p>5x - 2(5 - x) = 13&nbsp;</p><p>5x - 10 + 2x = 13</p><p>7x = 13 + 10</p><p>7x = 23</p><p>x = 23/7</p><p>&nbsp;</p><p>Substitusikan x = 23/7 ke persamaan (5)</p><p>y = 5 - x</p><p>y = 5 - 23/7</p><p>&nbsp; &nbsp; = 35/7 - 23/7</p><p>&nbsp; &nbsp; = 12/7</p><p>Substitusikan x = 23/7 dan y = 12/7 ke persamaan (3)</p><p>3x - y - z = 9&nbsp;</p><p>3(23/7) &nbsp;- 12/7 - z = 9&nbsp;</p><p>69/7 - 12/7 - z = 9</p><p>57/7 - z = 9</p><p>z = 57/7 - 9</p><p>&nbsp; &nbsp;= 57/7 - 63/7</p><p>&nbsp; &nbsp;= -6/7</p><p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p>