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.

---

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

---

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 $q=\dfrac1{y+1}$

$\begin{aligned}2p+q&=-6\\-2p+2q&=9\qquad+\\\hline3q&=3\\q&=1\\\dfrac1{y+1}&=1\\y+1&=1\\y&=0\\b&=0\end{aligned}$

$\begin{aligned}2p+q&=-6\\2p+1&=-6\\2p&=-7\\p&=-\dfrac72\\\dfrac1{x-1}&=-\dfrac72\\x-1&=-\dfrac27\\x&=1-\dfrac27\\a&=\dfrac57\end{aligned}$

$\begin{aligned}7a+2b&=7\left(\dfrac57\right)+2(0)\\&=\boxed{\boxed{5}}\end{aligned}$

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

---

No. 2

Jika $a$ dan $b$ memenuhi

Share this post