Berikut ini adalah kumpulan soal mengenai Sistem Persamaan tingkat SBMPTN. Jika ada jawaban yang salah, mohon dikoreksi melalui komentar. Terima kasih.
No. 1
Jika
A dan
B memenuhi \begin{cases}\dfrac{3A}{2A+3B}+\dfrac{6B}{2A-3B}=3\\[8pt]\dfrac{-6A}{2A+3B}+\dfrac{3B}{2A-3B}=-1\end{cases} maka
\dfrac{AB}{4A^2-9B^2}= ....
- >-\dfrac23
- -\dfrac13
- -\dfrac19
Misal {x=\dfrac{A}{2A+3B}} dan {y=\dfrac{B}{2A-3B}}
\(\begin{array}{rl|l}
3x+6y&=3&\times2\\
-6x+3y&=-1&\times1
\end{array}\)
\(\eqalign{
6x+12y&=6\\
-6x+3y&=-1\qquad+\\\hline
15y&=5\\
y&=\dfrac13\\
\dfrac{B}{2A-3B}&=\dfrac13
}\)
\(\eqalign{
3x+6y&=3\\
3x+6\left(\dfrac13\right)&=3\\
3x+2&=3\\
x&=\dfrac13\\
\dfrac{A}{2A+3B}&=\dfrac13
}\)
\(\eqalign{
\dfrac{AB}{4A^2-9B^2}&=\left(\dfrac{A}{2A+3B}\right)\left(\dfrac{B}{2A-3B}\right)\\[4pt]
&=\left(\dfrac13\right)\left(\dfrac13\right)\\[4pt]
&=\dfrac19
}\)
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=} ....
\(\eqalign{
\dfrac{2x+y}{3x-2y+3}&=\dfrac1{15}\\
15(2x+y)&=3x-2y+3\\
30x+15y&=3x-2y+3\\
27x+17y&=3
}\)
\(\eqalign{
\dfrac1{x+y}&=\dfrac7{-2x+y}\\
-2x+y&=7x+7y\\
-9x&=6y\\
3x+2y&=0
}\)
\(\begin{array}{rl|l}
27x+17y&=3&\times1\\
3x+2y&=0&\times9
\end{array}\)
\(\eqalign{
27x+17y&=3\\
27x+18y&=0\qquad-\\\hline
-y&=3\\
y&=-3
}\)
\(\eqalign{
3x+2y&=0\\
3x+2(-3)&=0\\
x&=2
}\)
\(\eqalign{
x-y&=2-(-3)\\
&=5
}\)
No. 3
Jika
{ax+y=4},
{x+by=7}, dan
{ab=2}, maka nilai
{2ax-3y=}
- {28-32a}
- {28-35a}
- {28-38a}
\(\begin{aligned}
x+by&=7&\qquad\color{red}{\times a}\\
ax+aby&=7a\\
ax+2y&=7a
\end{aligned}\)
(\begin{aligned}
ax+y&=4&\qquad\color{red}{\times 7}\\
ax+2y&=7a&\qquad\color{red}{\times 5}
\end{aligned}\)
\(\begin{aligned}
7ax+7y&=28\\
5ax+10y&=35a&\qquad\color{red}{-}\\\hline
2ax-3y&=\boxed{\boxed{28-35a}}
\end{aligned}\)
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