Exercise Zone : Sistem Persamaan Aljabar

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Berikut ini adalah kumpulan soal mengenai Sistem Persamaan Aljabar. Jika ingin bertanya soal, silahkan gabung ke grup Telegram, Signal, Discord, atau WhatsApp.

Tipe:

StandarSNBTHOTS

No.

Jika x dan y memenuhi 3^{x + 1} − 3⋅2^y = −3 dan 2⋅3^x + 2^y = 10, maka x + y = ....

1. 5
2. 4
3. 3

4. 2
5. 1

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ALTERNATIF PENYELESAIAN

\begin{aligned} 3^{x+1}-3\cdot2^xy&=-3\\ 3^x\cdot3^1-3\cdot2^y&=-3\\ 3\cdot3^x-3\cdot2^y&=-3\\ 3^x-2^y&=-1 \end{aligned} \begin{aligned} 3^x-2^y&=-1\\ 2\cdot3^x+2^y&=10\qquad&+\\\hline 3\cdot3^x&=9\\ 3^x&=3\\ x&=1 \end{aligned}

\begin{aligned} 3^x-2^y&=-1\\ 3-2^y&=-1\\ -2^y&=-4\\ 2^y&=4\\ 2^y&=2^2\\ y&=2 \end{aligned} \begin{aligned} x+y&=1+2\\ &=\boxed{\boxed{3}} \end{aligned}

Jadi, x + y = 3.
JAWAB: C

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No.

Diketahui x = a dan y = b memenuhi sistem persamaan \begin{cases} \dfrac2{x-1}+\dfrac1{y+1}=-6\\[4pt] \dfrac{-2}{x-1}+\dfrac2{y+1}=9 \end{cases} maka 7a + 2b =

1. 4
2. 5
3. 6

4. 7
5. 8

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ALTERNATIF PENYELESAIAN

Misal p=\dfrac1{x-1} dan q=\dfrac1{y+1} \begin{aligned} 2p+q&=-6\\ -2p+2q&=9\qquad+\\\hline 3q&=3\\ q&=1\\ \dfrac1{y+1}&=1\\ y+1&=1\\ y&=0\\ b&=0 \end{aligned}

\begin{aligned} 2p+q&=-6\\ 2p+1&=-6\\ 2p&=-7\\ p&=-\dfrac72\\ \dfrac1{x-1}&=-\dfrac72\\ x-1&=-\dfrac27\\ x&=1-\dfrac27\\ a&=\dfrac57 \end{aligned} \begin{aligned} 7a+2b&=7\left(\dfrac57\right)+2(0)\\ &=\boxed{\boxed{5}} \end{aligned}

Jadi, 7a + 2b = 5.
JAWAB: B

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No.

Nilai (x − y) yang memenuhi sistem persamaan 5x + 9y = 12 dan {\dfrac7{x+2}-\dfrac3{y+1}=0} adalah

1. \dfrac72
2. \dfrac94
3. 2

4. 1
5. \dfrac34

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ALTERNATIF PENYELESAIAN

\begin{aligned} \dfrac7{x+2}-\dfrac3{y+1}&=0\\[3.8pt] \dfrac7{x+2}&=\dfrac3{y+1}\\[3.8pt] 7(y+1)&=3(x+2)\\ 7y+7&=3x+6\\ -3x+7y&=-1 \end{aligned} \begin{aligned} 5x+9y&=12\qquad&\color{red}{\times3}\\ -3x+7y&=-1\qquad&\color{red}{\times5} \end{aligned} \begin{aligned} 15x+27y&=36\\ -15x+35y&=-5\qquad&\color{red}{+}\\\hline 62y&=31\\ y&=\dfrac{31}{62}\\[3.8pt] y&=\dfrac12 \end{aligned}

\begin{aligned} -3x+7\left(\dfrac12\right)&=-1\\[3.8pt] -3x+\dfrac72&=-1\\[3.8pt] -3x&=-1-\dfrac72\\[3.8pt] -3x&=-\dfrac92\\[3.8pt] x&=\dfrac32 \end{aligned} \begin{aligned} x-y&=\dfrac32-\dfrac12\\ &=\dfrac22\\ &=\boxed{\boxed{1}} \end{aligned}

Jadi, x − y = 1.
JAWAB: D

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