Exercise Zone : Sistem Persamaan

Berikut ini adalah kumpulan soal mengenai Sistem Persamaan tingkat dasar. Jika ada jawaban yang salah, mohon dikoreksi melalui komentar. Terima kasih.\

Tipe:

Standar SBMPTN HOTS

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No. 1

Jika x dan y memenuhi {3^{x+1}-3\cdot2^y=-3} dan {2\cdot3^x+2^y=10}, maka {x+y=} ....

1. 5
2. 4
3. 3

4. 2
5. 1

\(\eqalign{ 3^{x+1}-3\cdot2^xy&=-3\\ 3^x\cdot3^1-3\cdot2^y&=-3\\ 3\cdot3^x-3\cdot2^y&=-3\\ 3^x-2^y&=-1 }\)

\(\eqalign{ 3^x-2^y&=-1\\ 2\cdot3^x+2^y&=10\qquad&+\\\hline 3\cdot3^x&=9\\ 3^x&=3\\ x&=1 }\)

\(\eqalign{ 3^x-2^y&=-1\\ 3-2^y&=-1\\ -2^y&=-4\\ 2^y&=4\\ 2^y&=2^2\\ y&=2 }\)

\(\eqalign{ x+y&=1+2\\ &=\boxed{\boxed{3}} }\)

Jadi, x+y=3.
JAWAB: C

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No. 2

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

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=.
JAWAB: B

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No. 3

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

Grup Facebook

\(\begin{aligned} \dfrac7{x+2}-\dfrac3{y+1}&=0\\[8pt] \dfrac7{x+2}&=\dfrac3{y+1}\\[8pt] 7(y+1)&=3(x+2)\\ 7y+7&=3x+6\\ -3x+7y&=-1 \end{aligned}\)

\(\begin{aligned} 5x+9y&=12\qquad&\color{red}{\times3}\\ -3x+7y&=-1\qquad&\color{red}{\times5} \end{aligned}\)

\(\begin{aligned} 15x+27y&=36\\ -15x+35y&=-5\qquad&\color{red}{+}\\\hline\\[-10pt] 62y&=31\\ y&=\dfrac{31}{62}\\[8pt] y&=\dfrac12 \end{aligned}\)

\(\begin{aligned} -3x+7\left(\dfrac12\right)&=-1\\[8pt] -3x+\dfrac72&=-1\\[8pt] -3x&=-1-\dfrac72\\[8pt] -3x&=-\dfrac92\\[8pt] x&=\dfrac32 \end{aligned}\)

\(\begin{aligned} x-y&=\dfrac32-\dfrac12\\ &=\dfrac22\\ &=\boxed{\boxed{1}} \end{aligned}\)

Jadi, x-y=1.
JAWAB: D