tentukan himpunan penyelesaian dari sistem persamaan berikut dengan cara eliminasi a. 3( x + y ) - 2x = 19 dan 5x - 3( x + y ) = 22 b. 4( x - 3y ) + 7y =5 dan 9

a) 3( x + y ) - 2x = 19
3x + 3y - 2x = 19
x + 3y = 19 ... pers 1
5x - 3(x + y) = 22
5x - 3x - 3y = 22
2x - 3y = 22 ... pers 2

pers 1 & 2 dieliminasi
x + 3y = 19
2x - 3y = 22
------------------(+)
3x = 41
x = 41/3

x + 3y = 19 |×2
2x - 3y = 22
maka
2x + 6y = 38
2x - 3y = 22
--------------------(-)
9y = 16
y = 16/9

hp = { 41/3 , 16/9 }

b) 4 ( x - 3y) + 7y = 5
4x - 12y + 7y = 5
4x - 5y = 5 ... pers 1
9y - 4 ( x - 3y ) = 43
9y - 4x + 12y = 43
21y - 4x = 43
- 4x + 21y = 43 ... pers 2

pers 1 & 2 dieliminasi
4x - 5y = 5
- 4x + 21y = 43
---------------------(+)
16y = 48
y = 3

pers 1 & 2
4x - 5y = 5 |×21
- 4x + 21y = 43 |×5
maka
84x - 105y = 105
- 20x + 105y = 215
-----------------------------(+)
64x = 320
x = 5

hp = ( 5 , 3 )

[tex]$\begin{align}-2x+3(x+y)&=19\\\underline{5x-3(x+y)}&\underline{\ =22\ \ +}\\3x&=41\\x&=\frac{41}3=13\frac23\end[/tex]


[tex]$\begin{align}-2x+3(x+y)&=19\\-2x+3x+3y&=19\\x+3y&=19&&\to\text{kalikan 2}\\2x+6y&=38\\\\5x-3(x+y)&=22\\5x-3x-3y&=22\\2x-3y&=22\\\\2x+6y&=38\\\underline{2x-3y}&\underline{\ =22\ \ -}\\9y&=16\\y&=\frac{16}9=1\frac79\end[/tex]


[tex]\boxed{\text{HP}=\left\{13\frac23,\ 1\frac79\right\}}[/tex]
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[tex]$\begin{align}4(x-3y)+7y&=\ \ 5\\\underline{-4(x-3y)+9y}&\underline{\ =43\ \ +}\\16y&=48\\y&=\ \ 3\end[/tex]


[tex]$\begin{align}4(x-3y)+7y&=5\\4x-12y+7y&=5\\4x-5y&=5&&\to\text{kalikan 21}\\84x-105y&=105\\\\-4(x-3y)+9y&=43\\-4x+12y+9y&=43\\-4x+21y&=43&&\to\text{kalikan 5}\\-20x+105y&=215\\\\84x\ -\ 105y&=105\\\underline{-20x+105y}&\underline{\ =215\ \ +}\\28x&=320\\x&=\ \ \ 5\end[/tex]


[tex]\boxed{\text{HP}=\{5,\ 3\}}[/tex]



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