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

$\begin{array}{rl}{3}^{x+1}-3\cdot 2^{x}y& =-3\\ 3^x\cdot 3^1-3\cdot 2^y& =-3\\ 3\cdot 3^x-3\cdot 2^y& =-3\\ 3^x-2^y& =-1\end{array}$

$\begin{array}{rl}{3}^x-2^y& =-1\\ 2\cdot 3^x+2^y& =10& +\\ 3\cdot 3^x& =9\\ 3^x& =3\\ x& =1\end{array}$

$\begin{array}{rl}{3}^x-2^y& =-1\\ 3-2^y& =-1\\ -2^y& =-4\\ 2^y& =4\\ 2^y& =2^2\\ y& =2\end{array}$

$\begin{array}{rl}x+y& =1+2\\ & =\boxed{{\displaystyle \boxed{{\displaystyle 3}}}}\end{array}$

Jadi, x+y=3.
JAWAB: C

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No. 2

Diketahui x=a dan y=b memenuhi sistem persamaan $$\{\begin{array}{l}{\displaystyle \frac{2}{x-1}}+{\displaystyle \frac{1}{y+1}}=-6\\ {\displaystyle \frac{-2}{x-1}}+{\displaystyle \frac{2}{y+1}}=9\end{array}$$ maka 7a+2b=

1. 4
2. 5
3. 6

4. 7
5. 8

Misal p=\dfrac1{x-1} dan q=\dfrac1{y+1}

$\begin{array}{rl}2p+q& =-6\\ -2p+2q& =9+\\ 3q& =3\\ q& =1\\ {\displaystyle \frac{1}{y+1}}& =1\\ y+1& =1\\ y& =0\\ b& =0\end{array}$

$\begin{array}{rl}2p+q& =-6\\ 2p+1& =-6\\ 2p& =-7\\ p& =-{\displaystyle \frac{7}{2}}\\ {\displaystyle \frac{1}{x-1}}& =-{\displaystyle \frac{7}{2}}\\ x-1& =-{\displaystyle \frac{2}{7}}\\ x& =1-{\displaystyle \frac{2}{7}}\\ a& ={\displaystyle \frac{5}{7}}\end{array}$

$\begin{array}{rl}7a+2b& =7\left({\displaystyle \frac{5}{7}}\right)+2(0)\\ & =\boxed{{\displaystyle \boxed{{\displaystyle 5}}}}\end{array}$

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

$\begin{array}{rl}{\displaystyle \frac{7}{x+2}}-{\displaystyle \frac{3}{y+1}}& =0\\ {\displaystyle \frac{7}{x+2}}& ={\displaystyle \frac{3}{y+1}}\\ 7(y+1)& =3(x+2)\\ 7y+7& =3x+6\\ -3x+7y& =-1\end{array}$

$\begin{array}{rlr}5x+9y& =12& \times 3\\ -3x+7y& =-1& \times 5\end{array}$

$\begin{array}{rl}15x+27y& =36\\ -15x+35y& =-5& +\\ \\ 62y& =31\\ y& ={\displaystyle \frac{31}{62}}\\ y& ={\displaystyle \frac{1}{2}}\end{array}$

$\begin{array}{rl}-3x+7\left({\displaystyle \frac{1}{2}}\right)& =-1\\ -3x+{\displaystyle \frac{7}{2}}& =-1\\ -3x& =-1-{\displaystyle \frac{7}{2}}\\ -3x& =-{\displaystyle \frac{9}{2}}\\ x& ={\displaystyle \frac{3}{2}}\end{array}$

$\begin{array}{rl}x-y& ={\displaystyle \frac{3}{2}}-{\displaystyle \frac{1}{2}}\\ & ={\displaystyle \frac{2}{2}}\\ & =\boxed{{\displaystyle \boxed{{\displaystyle 1}}}}\end{array}$

Jadi, x-y=1.
JAWAB: D