1. Tentukan himpunan penyelesaian dari sistem persamaan linear tiga variabel berikut dengan metode eliminasi (2x + y + 3z = 2 ) ( x - y + 2z = -4 ) ( x + 3y - z = 1 2 . Tentukan himpunan penyelesaian dari sistem persamaan linear tiga variabel berikut dengan metode gabungan (eliminasi-subsitusi) 2x + 3y + z = 13 -3x + 2y + z = -4 4x-4y+z= 5

<p><strong>Jadi, jawaban yang tepat adalah</strong></p><p><strong>1. x = -9, y = 5, z = 5</strong></p><p><strong>2. x = 3, y = 2, z = 1</strong></p><p><strong>Pembahasan:&nbsp;</strong></p><p>1. Tertera pada gambar, ya!</p><p>2.&nbsp;</p><p><strong>• Metode Eliminasi&nbsp;</strong></p><p>2x + 3y + z = 13</p><p>-3x + 2y + z = -4</p><p>4x - 4y + z = 5</p><p>&nbsp;</p><p>2x + 3y + z = 13</p><p>-3x + 2y + z = -4</p><p>——————————¯</p><p><strong>5x + y &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 17</strong></p><p>&nbsp;</p><p>-3x + 2y + z = -4</p><p>4x - 4y + z = 5</p><p>——————————¯</p><p><strong>-7x + 6y &nbsp; &nbsp; &nbsp;= -9</strong></p><p>&nbsp;</p><p>5x + y = 17 &nbsp; &nbsp;|x6| &nbsp;30x +6y = 102</p><p>-7x + 6y = -9 &nbsp;|X1| &nbsp;-7x + 6y = -9</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; 37x &nbsp; &nbsp; &nbsp; &nbsp;= 111</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; x &nbsp; &nbsp; &nbsp;= 111/37</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<strong>x &nbsp; &nbsp; = 3</strong></p><p><strong>• Metode Substitusi</strong></p><p>5x + y = 17</p><p>5(3) + y = 17</p><p>15 + y = 17</p><p>y = 17 - 15</p><p><strong>y = 2</strong></p><p>&nbsp;</p><p>4x - 4y + z = 5</p><p>4(3) - 4(2) + z = 5</p><p>12 - 8 + z = 5</p><p>4 + z = 5</p><p>z = 5 - 4&nbsp;</p><p><strong>z = 1</strong></p><p>&nbsp;</p><p><strong>Jadi, Himpunan Penyelesaiannya adalah x = 3, y = 2, z = 1</strong></p><p>&nbsp;</p><p>Semoga membantu dan semangat belajar!</p>