Cari HT persamaan berikut : 1. 2. 3. 4. Jawab dengan caranya.... Question from @Yusuef

October 2018 1 119 Report

Cari HT persamaan berikut :
1. $\left \{ {{x-y=-1} \atop {x-y=3}} \right.$
2. $\left \{ {{2x-y=5} \atop {2x-3y=-1}} \right.$
3. $\left \{ {{2x+3y=9} \atop {3x-3y=16}} \right.$
4. $\left \{ {{2x+y=12} \atop {3x-2y=25}} \right.$

Jawab dengan caranya

Takamori37 $\boxed{\begin{array}{l}\texttt{Untuk persamaan linear dua variabel digambarkan dalam:} \\ a_1x+b_1y=c_1 \\ a_2x+b_2y=c_2 \\\\ \texttt{Dapat dijadikan bentuk matriks menjadi:} \\ \left[\begin{array}{cc}a_1&b_1 \\ a_2&b_2\end{array}\right]\left[\begin{array}{cc}x\\y\end{array}\right]=\left[\begin{array}{cc}c_1\\c_2\end{array}\right]\end{array}}$

Dengan demikian:

Nomor 1.
$$\begin{align} \left[\begin{array}{cc}1&-1 \\ 1&-1\end{array}\right]\left[\begin{array}{cc}x\\y\end{array}\right]&=\left[\begin{array}{cc}-1\\3\end{array}\right] \\ \left[\begin{array}{cc}x\\y\end{array}\right]&=\left[\begin{array}{cc}1&-1 \\ 1&-1\end{array}\right]^{-1}\left[\begin{array}{cc}-1\\3\end{array}\right] \\ \left[\begin{array}{cc}x\\y\end{array}\right]&=\frac{1}{1(-1)-1(-1)}\left[\begin{array}{cc}-1&1 \\ -1&1\end{array}\right]\left[\begin{array}{cc}-1\\3\end{array}\right] \end{align}$
Karena pada pecahan skalar menghasilkan 1/0
Maka, tidak ada penyelesaian atau himpunan kosong.

Nomor 2.
$$\begin{align} \left[\begin{array}{cc}2&-1 \\ 2&-3\end{array}\right]\left[\begin{array}{cc}x\\y\end{array}\right]&=\left[\begin{array}{cc}5\\-1\end{array}\right] \\ \left[\begin{array}{cc}x\\y\end{array}\right]&=\left[\begin{array}{cc}2&-1 \\ 2&-3\end{array}\right]^{-1}\left[\begin{array}{cc}5\\-1\end{array}\right] \\ \left[\begin{array}{cc}x\\y\end{array}\right]&=\frac{1}{-4}\left[\begin{array}{cc}-3&1 \\ 2&2\end{array}\right]\left[\begin{array}{cc}5\\-1\end{array}\right] \\ \end{align}$
Kalikan menjadi:
$\displaystyle\left[\begin{array}{cc}x\\y\end{array}\right]&=\frac{1}{-4}\left[\begin{array}{cc}-16\\ 8\end{array}\right] \\\\ \left[\begin{array}{cc}x\\y\end{array}\right]&=\left[\begin{array}{cc}4\\ -2\end{array}\right]$

Nomor 3.
$$\begin{align} \left[\begin{array}{cc}2&3 \\ 3&-3\end{array}\right]\left[\begin{array}{cc}x\\y\end{array}\right]&=\left[\begin{array}{cc}9\\16\end{array}\right]
 \\ 
\left[\begin{array}{cc}x\\y\end{array}\right]&=\left[\begin{array}{cc}2&3\\3&-3\end{array}\right]^{-1}\left[\begin{array}{cc}9\\16\end{array}\right]
 \\ 
\left[\begin{array}{cc}x\\y\end{array}\right]&=\frac{1}{-15}\left[\begin{array}{cc}-3&-3
 \\ -3&2\end{array}\right]\left[\begin{array}{cc}9\\16\end{array}\right] 
\\ \end{align}$
Kalikan menjadi:
$\displaystyle\left[\begin{array}{cc}x\\y\end{array}\right]&=\frac{1}{-15}\left[\begin{array}{cc}-75\\5\end{array}\right] \\\\ 
\left[\begin{array}{cc}x\\y\end{array}\right]&=\left[\begin{array}{cc}5\\
 -1/3\end{array}\right]$

Nomor 4.
$$\begin{align} \left[\begin{array}{cc}2&1 \\ 
3&-2\end{array}\right]\left[\begin{array}{cc}x\\y\end{array}\right]&=\left[\begin{array}{cc}12\\25\end{array}\right]

 \\ 
\left[\begin{array}{cc}x\\y\end{array}\right]&=\left[\begin{array}{cc}2&1\\3&-2\end{array}\right]^{-1}\left[\begin{array}{cc}12\\25\end{array}\right]

 \\ 
\left[\begin{array}{cc}x\\y\end{array}\right]&=\frac{1}{-7}\left[\begin{array}{cc}-2&-1

 \\ 
-3&2\end{array}\right]\left[\begin{array}{cc}12\\25\end{array}\right]
 
\\ \end{align}$
Kalikan menjadi:
$\displaystyle\left[\begin{array}{cc}x\\y\end{array}\right]&=\frac{1}{-7}\left[\begin{array}{cc}-49\\14\end{array}\right]
 \\\\ 
\left[\begin{array}{cc}x\\y\end{array}\right]&=\left[\begin{array}{cc}7\\

 -2\end{array}\right]$

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