Tentukan himpunan penyelesaian -x+2y+z=4 2x+3y-4z=15 3x-5y+z=-13

<p>Ada 3 persamaan :</p><p>-x+2y+z=4 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (i)</p><p>2x+3y-4z=15 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;(ii)</p><p>3x-5y+z=-13 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (iii)</p><p>&nbsp;</p><p>Kita selesaikan dulu (i) dan (ii), kita samakan variabel x.</p><p>-x+2y+z=4 &nbsp; &nbsp; &nbsp; &nbsp; (x2) &nbsp;--&gt; -2x+4y+2z=8 &nbsp;&nbsp;</p><p>2x+3y-4z=15 &nbsp; &nbsp;(x1) &nbsp;--&gt; <u>2x+3y-4z=15</u> &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; 7y-2z=23 &nbsp; &nbsp; &nbsp;(iv)</p><p>&nbsp;</p><p>Hal yang sama pada (i) dan (iii), kita samakan juga variabel x.</p><p>-x+2y+z=4 &nbsp; &nbsp; &nbsp; &nbsp; (x3) &nbsp;--&gt; -3x+6y+3z=12 &nbsp;</p><p>3x-5y+z=-13 &nbsp; &nbsp; (x1) &nbsp;--&gt; <u>3x-5y+z=-13</u> &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; y + 4z = -1 &nbsp; (v)</p><p>&nbsp;</p><p>Kemudian dicari penyelesaian (iv) dan (v)</p><p>7y-2z=23 &nbsp; &nbsp; &nbsp;(x2) --&gt; 14y-4z = 46</p><p>&nbsp; y + 4z = -1 &nbsp; (x1) --&gt; &nbsp;<u> y + 4z = -1</u> &nbsp;+</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;15y = 45</p><p>Sehingga y = 45/15 = 3</p><p>&nbsp;</p><p>Dari (v) kita cari z :</p><p>y + 4z = -1</p><p>3 + 4z = -1</p><p>4z = -1 -3 = 4</p><p>z = -1</p><p>&nbsp;</p><p>Dari (i) kita cari x :</p><p>-x+2y+z=4 &nbsp;</p><p>-x + 2.3 + (-1) = 4</p><p>-x + 5 =4</p><p>-x = 5 - 4 =1</p><p>&nbsp;</p><p>Sehingga himpunan penyelesaiannya adalah x=1, y=3 dan z= -1</p><p>Semoga membantu.</p><p>&nbsp;</p>