Dibantu menjawab soal sistem persamaan linear tiga variable

<p>Ada 3 persamaan :</p><p>4x + y + z = 11 &nbsp; (i)<br>x + 4y + z = 11 &nbsp; (ii)<br>x + y + 4z = 8 &nbsp; &nbsp;(iii)</p><p>&nbsp;</p><p>Kita selesaikan dulu (ii) dan (i). Letak kita sesuaikan untuk mempermudah perhitungan kita.</p><p>x + 4y + z = 11 &nbsp; &nbsp;(x4) --&gt; 4x + 16y + 4z = 44<br>4x + y + z = 11 &nbsp; &nbsp;(x1) --&gt; <u>4x + y + z = 11</u> &nbsp;-<br>&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; 15y + 3z = 33 &nbsp; &nbsp; (iv)</p><p>&nbsp;</p><p>Hal yang sama pada persamaan (ii) dan (iii),&nbsp;</p><p>x + 4y + z = 11<br><u>x + y + 4z = 8</u> &nbsp;-<br>3y - 3z = 3 &nbsp; &nbsp; (v)</p><p>&nbsp;</p><p>Dari (iv) dan (v), kita bisa selesaikan :</p><p>15y + 3z = 33 &nbsp;(x1) --&gt; 15y + 3z = 33<br>3y - 3z = 3 &nbsp; &nbsp; &nbsp; &nbsp;(x5) --&gt; <u>15y - 15z = 15</u> &nbsp;-<br>&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; &nbsp;18z=18<br>&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; &nbsp; &nbsp; z=1</p><p>&nbsp;</p><p>Dari persamaan (v), kita bisa hitung y</p><p>3y - 3z = 3<br>3y - 3.1 = 3<br>3y = 3 + 3 =6<br>y=2</p><p>&nbsp;</p><p>Dari persamaan (iii), kita bisa hitung x</p><p>x+y+4z = 8<br>x+2+4=8<br>x+6=8</p><p>x=8-6 = 2<br>&nbsp;</p><p>Sehingga jawabannya adalah {(2,2,1)} &nbsp;... <strong>C</strong></p><p>Semoga membantu.</p>