SBMPTN Zone : Sistem Persamaan

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

Tipe:

Standar SBMPTN HOTS

No. 1

Jika A dan B memenuhi $$\{\begin{array}{l}{\displaystyle \frac{3A}{2A+3B}}+{\displaystyle \frac{6B}{2A-3B}}=3\\ {\displaystyle \frac{-6A}{2A+3B}}+{\displaystyle \frac{3B}{2A-3B}}=-1\end{array}$$ maka \dfrac{AB}{4A^2-9B^2}= ....

1. -\dfrac23
2. -\dfrac13
3. -\dfrac19

4. \dfrac19
5. \dfrac13

SBMPTN 2017

Misal {x=\dfrac{A}{2A+3B}} dan {y=\dfrac{B}{2A-3B}}

$\begin{array}{rll}3x+6y& =3& \times 2\\ -6x+3y& =-1& \times 1\end{array}$

$\begin{array}{rl}6x+12y& =6\\ -6x+3y& =-1+\\ 15y& =5\\ y& ={\displaystyle \frac{1}{3}}\\ {\displaystyle \frac{B}{2A-3B}}& ={\displaystyle \frac{1}{3}}\end{array}$

$\begin{array}{rl}3x+6y& =3\\ 3x+6\left({\displaystyle \frac{1}{3}}\right)& =3\\ 3x+2& =3\\ x& ={\displaystyle \frac{1}{3}}\\ {\displaystyle \frac{A}{2A+3B}}& ={\displaystyle \frac{1}{3}}\end{array}$

$\begin{array}{rl}{\displaystyle \frac{AB}{4A^2-9B^2}}& =\left({\displaystyle \frac{A}{2A+3B}}\right)\left({\displaystyle \frac{B}{2A-3B}}\right)\\ & =\left({\displaystyle \frac{1}{3}}\right)\left({\displaystyle \frac{1}{3}}\right)\\ & ={\displaystyle \frac{1}{9}}\end{array}$

JAWAB: D

No. 2

Jika x dan y memenuhi {\dfrac{2x+y}{3x-2y+3}=\dfrac1{15}} dan {\dfrac1{x+y}=\dfrac7{-2x+y}} maka nilai {x-y=} ....

$\begin{array}{rl}{\displaystyle \frac{2x+y}{3x-2y+3}}& ={\displaystyle \frac{1}{15}}\\ 15(2x+y)& =3x-2y+3\\ 30x+15y& =3x-2y+3\\ 27x+17y& =3\end{array}$

$\begin{array}{rl}{\displaystyle \frac{1}{x+y}}& ={\displaystyle \frac{7}{-2x+y}}\\ -2x+y& =7x+7y\\ -9x& =6y\\ 3x+2y& =0\end{array}$

$\begin{array}{rll}27x+17y& =3& \times 1\\ 3x+2y& =0& \times 9\end{array}$

$\begin{array}{rl}27x+17y& =3\\ 27x+18y& =0-\\ -y& =3\\ y& =-3\end{array}$

$\begin{array}{rl}3x+2y& =0\\ 3x+2(-3)& =0\\ x& =2\end{array}$

$\begin{array}{rl}x-y& =2-(-3)\\ & =5\end{array}$

Jadi, x-y=5.

No. 3

Jika {ax+y=4}, {x+by=7}, dan {ab=2}, maka nilai {2ax-3y=}

1. {28-32a}
2. {28-35a}
   
3. {28-38a}
   

4. {28-40a}
5. {28-46a}
   

$\begin{array}{rlr}x+by& =7& \times a\\ ax+aby& =7a\\ ax+2y& =7a\end{array}$

($$\begin{array}{rlr}ax+y& =4& \times 7\\ ax+2y& =7a& \times 5\end{array}$$\)

$\begin{array}{rl}7ax+7y& =28\\ 5ax+10y& =35a& -\\ 2ax-3y& =\boxed{{\displaystyle \boxed{{\displaystyle 28-35a}}}}\end{array}$

Jadi, 2ax-3y=28-35a.
JAWAB: B

No. 4

Jika 3x-2y = 4 dan \dfrac{216^x}{72^y} = 162, maka nilai dari y adalah . . .

1. -1
2. 0
3. 1

4. 2
5. 3

$\begin{array}{rl}{\displaystyle \frac{{216}^x}{{72}^y}}& =162\\ {\displaystyle \frac{{\left(6^3\right)}^x}{{(2\cdot 6^2)}^y}}& =162\\ {\displaystyle \frac{6^{3x}}{2^y\cdot 6^{2y}}}& =162\\ {\displaystyle \frac{6^{3x-2y}}{2^y}}& =2\cdot 81\\ {\displaystyle \frac{6^4}{2^y}}& =2\cdot 3^4\\ 2^y& ={\displaystyle \frac{6^4}{2\cdot 3^4}}\\ & ={\displaystyle \frac{2^4\cdot 3^4}{2\cdot 3^4}}\\ & =2^3\\ y& =3\end{array}$

Jadi, y=3.
JAWAB: E

No. 5

Jika a dan b memenuhi $$\{\begin{array}{ll}{\displaystyle \frac{2}{2a-b}}+{\displaystyle \frac{7}{2a+b}}& =3\\ {\displaystyle \frac{1}{2a-b}}-{\displaystyle \frac{7}{2a+b}}& =0\end{array}$$ maka {a+b=}

1. 5
2. 6
3. 7

4. 8
5. 9

SKMP Juli 2020

$\begin{array}{rl}{\displaystyle \frac{2}{2a-b}}+{\displaystyle \frac{7}{2a+b}}& =3\\ {\displaystyle \frac{1}{2a-b}}-{\displaystyle \frac{7}{2a+b}}& =0& +\\ {\displaystyle \frac{3}{2a-b}}& =3\\ 2a-b& =1\end{array}$

$\begin{array}{rl}{\displaystyle \frac{2}{2a-b}}+{\displaystyle \frac{7}{2a+b}}& =3\\ {\displaystyle \frac{2}{1}}+{\displaystyle \frac{7}{2a+b}}& =3\\ 2+{\displaystyle \frac{7}{2a+b}}& =3\\ {\displaystyle \frac{7}{2a+b}}& =1\\ 2a+b& =7\end{array}$

$\begin{array}{rl}2a-b& =1\\ 2a+b& =7& +\\ 4a& =8\\ 2a& =4\\ a& =2\end{array}$

$\begin{array}{rl}2a+b& =7\\ 4+b& =7\\ b& =3\end{array}$

$\begin{array}{rl}a+b& =2+3\\ & =\boxed{{\displaystyle \boxed{{\displaystyle 5}}}}\end{array}$

Jadi, {a+b=5}.