Tentukan hp dari x+2y+4z=5 2x+y-3z=1 3x+4y+2z=9

<p>HP = {(x ,y, z)} =<strong> {(-1, 3, 0)}</strong></p><p>&nbsp;</p><p><strong>Diketahui :</strong></p><p>&nbsp;&nbsp;x + 2y + 4z = 5&nbsp; ... (1)&nbsp;</p><p>&nbsp;&nbsp;&nbsp;2x + y - 3z = 1&nbsp; ... (2)&nbsp;</p><p>3x + 4y + 2z = 9 ... (3)</p><p><strong>Ditanya : </strong>HP =...?</p><p><strong>Dijawab :</strong></p><p>Mengurangi persamaan (1) dan (2) untuk eliminasi y:</p><p>x + 2y + 4z = 5 |1×| &nbsp; x + 2y + 4z = 5</p><p>2x + y - 3z = 1&nbsp; |2×| <u>4x + 2y - 6z = 2&nbsp;</u> –</p><p>ㅤㅤㅤㅤㅤㅤㅤㅤㅤ-3x + 0 + 10z = 3</p><p>-3x + 10z = 3 ... (4)</p><p>Mengurangi persamaan (1) dan (3) untuk eliminasi y:</p><p>&nbsp;&nbsp;x + 2y + 4z = 5 |2×| 2x + 4y + 8z = 10</p><p>3x + 4y + 2z = 9 |1×|&nbsp; <u>3x + 4y + 2z = 9&nbsp;</u> –</p><p>ㅤㅤㅤㅤㅤㅤㅤㅤㅤ &nbsp; &nbsp; -x + 0 + 6z = 1</p><p>-x + 6z = 1</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;-x = 1 - 6z</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;x = -1 + 6z ... (5)</p><p>Subtitusi x = -1 + 6z ke persamaan (4) :</p><p>-3x + 10z = 3&nbsp;</p><p>-3(-1 + 6z) + 10z = 3&nbsp;</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3 + -6z + 10z = 3</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;4z = 3 - 3</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;4z = 0</p><p>z = ⁰/₄</p><p><strong>z = 0</strong></p><p>Subtitusi z = 0 ke persamaan (5) :</p><p>x = -1 + 6z</p><p>x = -1 + 6.0</p><p><strong>x = -1</strong></p><p>Subtitusi x = -1 dan z = 0 ke (1) :</p><p>x + 2y + 4z = 5</p><p>-1 + 2y + 4.0 = 5</p><p>&nbsp;&nbsp;&nbsp;-1 + 2y + 0 = 5</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2y = 5 + 1</p><p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;2y = 6</p><p>y = ⁶/₂</p><p><strong>y = 3</strong></p><p>&nbsp;</p><p>Selesai :D 🙏</p><p>Maaf sering upload ulang :(🙏</p>