Elvara L

13 Januari 2023 01:13

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Elvara L

13 Januari 2023 01:13

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Nanda R

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13 Januari 2023 02:58

<p>2x-5y+3z=-10 ... (1)<br>3x+4y+7z=11 ... (2)<br>5x+3z+7z=-8 &nbsp;... (3)</p><p>&nbsp;</p><p>#Eliminasi variabel z pada persamaan (1) dan (2)<br>2x &nbsp;- 5y &nbsp;+ 3z = -10 &nbsp; | ×7<br>3x + 4y &nbsp;+ 7z = 11 &nbsp; &nbsp; | ×3<br>__________________<br>14x-35y+21z=-70<br>9x+12y+21z=-33<br>_________________-<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 5x-47y=-37 ... (4)</p><p>#Eliminasi variabel z pada persamaan (2) dan (3)<br>3x+4y+7z=11<br>5x+3z+7z=-8&nbsp;<br>_____________ -<br>&nbsp; &nbsp; &nbsp; &nbsp;-2x+y=-3 &nbsp;... (5)</p><p>#Eliminasi x pada persamaan (4) dan (5)<br>5x-47y=-37 &nbsp; &nbsp;| ×2<br>-2x &nbsp; +y=-3 &nbsp; &nbsp; &nbsp;| ×5<br>______________<br>10x-94y=-74<br>-10x+5y=-15<br>_____________+<br>&nbsp; &nbsp; &nbsp; -84y=-84<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; y=-84/-84<br>&nbsp; &nbsp;<strong> &nbsp; &nbsp; &nbsp; &nbsp; y=1</strong></p><p>&nbsp;</p><p>#Substitusi y=1 ke persamaan (5)<br>-2x+y=-3<br>-2x+1=-3<br>&nbsp; &nbsp; -2x=-3-1<br>&nbsp; &nbsp; -2x=-4<br>&nbsp; &nbsp; &nbsp; &nbsp;x=-4/-2<br>&nbsp; &nbsp; &nbsp;&nbsp;<strong> x=2</strong></p><p>&nbsp;</p><p>#Substitusi x=2 dan y=1 ke persamaan (1)<br>&nbsp; &nbsp; &nbsp; &nbsp;2x-5y+3z=-10<br>2(2)-5(1)+3z=-10<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;4-5+3z=-10<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;-1+3z=-10<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3z=-10+1<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 3z=-9<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; z=-9/3<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<strong>z=-3</strong></p><p>&nbsp;</p><p><strong>Jadi, HP={2,1,-3}</strong></p>

2x-5y+3z=-10 ... (1)
3x+4y+7z=11 ... (2)
5x+3z+7z=-8  ... (3)

 

#Eliminasi variabel z pada persamaan (1) dan (2)
2x  - 5y  + 3z = -10   | ×7
3x + 4y  + 7z = 11     | ×3
__________________
14x-35y+21z=-70
9x+12y+21z=-33
_________________-
          5x-47y=-37 ... (4)

#Eliminasi variabel z pada persamaan (2) dan (3)
3x+4y+7z=11
5x+3z+7z=-8 
_____________ -
       -2x+y=-3  ... (5)

#Eliminasi x pada persamaan (4) dan (5)
5x-47y=-37    | ×2
-2x   +y=-3      | ×5
______________
10x-94y=-74
-10x+5y=-15
_____________+
      -84y=-84
            y=-84/-84
            y=1

 

#Substitusi y=1 ke persamaan (5)
-2x+y=-3
-2x+1=-3
    -2x=-3-1
    -2x=-4
       x=-4/-2
       x=2

 

#Substitusi x=2 dan y=1 ke persamaan (1)
       2x-5y+3z=-10
2(2)-5(1)+3z=-10
           4-5+3z=-10
             -1+3z=-10
                    3z=-10+1
                    3z=-9
                      z=-9/3
                      z=-3

 

Jadi, HP={2,1,-3}


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