x+2y+2z=11 2x-y+2=5 x+2y+3z=16 tentukan x+y+z=..?

<p>1) eliminasi persamaan 1 dan 3</p><p>x + 2y + 2z = 11</p><p>x + 2y + 3z = 16</p><p>________________—</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; -z = -5 dikali (-1) maka z = 5</p><p>2) eliminasi persamaan 1 dan 2 menghasilkan persamaan 4&nbsp;</p><p>x + 2y + 2z = 11</p><p>2x - y + 2z = 5</p><p>_______________—</p><p>-x + 3y = 6 ... (iv)</p><p>3) eliminasi persamaan 1 dan 3 menghasilkan persamaan 5</p><p>x + 2y + 2z = 11 &nbsp;(×3) 3x + 6y + 6z = 33</p><p>x + 2y + 3z = 16 &nbsp;(×2) 2x + 4y + 6z = 32</p><p>&nbsp; &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; &nbsp; &nbsp; &nbsp; &nbsp;x + 2y &nbsp; = 1 ... (v)</p><p>4) eliminasi persamaan 4 dan 5&nbsp;</p><p>x + 2y = 1</p><p>-x + 3y = 6</p><p>___________+</p><p>&nbsp; &nbsp; &nbsp; &nbsp;5y = 7</p><p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;y = 7/5</p><p>5) substitusi nilai y = 7/5 dan z = 5 ke dalam persamaan 2</p><p>2x - y + 2z = 5</p><p>2x - 7/5 + 2(5) = 5</p><p>2x = 5 - 10 + 7/5</p><p>2x = 7/5 - 5</p><p>2x = 7/5 - 25/5</p><p>2x = -18/5</p><p>x = -9/5</p><p>jadi, nilai x = -9/5 ; y = 7/5 ; dan z = 5, maka</p><p>x + y + z = -9/5 + 7/5 + 5 = -5/5 + 5 = -1 + 5 = 4</p>