Latihan materi sistem persamaan linear tiga variabel Tentukan nilai x,y,dan z 3x+2y-z=14 X-y+2z=-1 2×+y+3z=5

<p><strong>Jawaban yang tepat adalah x = 3, y = 2, z = -1</strong></p><p>&nbsp;</p><p><strong>Pembahasan:</strong></p><p>3x + 2y - z = 14</p><p>x - y + 2z = -1</p><p>2x + y + 3z = 5</p><p>&nbsp;</p><p><strong>• Metode Eliminasi</strong></p><p>3x + 2y - z = 14 &nbsp;|x2| &nbsp;6x + 4y - 2z = 28</p><p>x - y + 2z = -1 &nbsp; &nbsp; |x1| &nbsp; &nbsp; x - y + 2z &nbsp; &nbsp;= -1</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &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; 7x + 3y &nbsp; &nbsp; = 27</p><p>&nbsp;</p><p>x - y + 2z = -1 &nbsp; &nbsp;|x3| &nbsp;3x - 3y + 6z = -3</p><p>2x + y + 3z = 5 &nbsp; |x2| &nbsp;4x + 2y + 6z = 10&nbsp;</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &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; -x &nbsp;- &nbsp;5y &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;= -13&nbsp;</p><p>&nbsp;</p><p>7x + 3y = 27 &nbsp; |x1| &nbsp;7x + 3y = 27</p><p>-x - 5y &nbsp; = -13 &nbsp;|x7| &nbsp;-7x - 35y = -91</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &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; -32y = -64</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;y = -64/-32</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<strong> &nbsp; y = 2&nbsp;</strong></p><p>&nbsp;</p><p>7x + 3y = 27 &nbsp;|x5| &nbsp;35x + 15y = 135</p><p>-x - 5y = -13 &nbsp; |x3| &nbsp;-3x - 15y &nbsp; = -39</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &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;32x &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 96</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;x = 96/32</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;<strong>x = 3&nbsp;</strong></p><p>&nbsp;</p><p><strong>• Metode Substitusi</strong></p><p>3x + 2y - z = 14</p><p>3(<strong>3</strong>) + 2(<strong>2</strong>) - z = 14</p><p>9 + 4 - z = 14</p><p>13 - z = 14</p><p>-z = 14 - 13</p><p>-z = 1</p><p><strong>z = -1&nbsp;</strong></p><p>&nbsp;</p><p><strong>Jadi, x = 3, y = 2, z = -1</strong></p><p>&nbsp;</p><p>&nbsp;</p><p>Semoga membantu dan semangat belajar!</p><p>&nbsp;</p>