2x - 3y = 4
X + 3y = 5
Tentukan Hp dengan cara:
1. Invers matriks
2. Determinan
X + 3y = 5
Tentukan Hp dengan cara:
1. Invers matriks
2. Determinan
IcukSugiarto
![\bold{\underline{\bigstar~Solution\ 1\ "Use\ Invers\ Matriks"}}\\\\2x-3y=4.......................[1]\\~~x+3y=5.......................[2]\\\\$Buat model matriksnya :$\\\\ \left[\begin{array}{ccc}2&-3\\1&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]=\left[\begin{array}{ccc}4\\5\end{array}\right]\\\\$Sehingga :$](https://tex.z-dn.net/?f=%5Cbold%7B%5Cunderline%7B%5Cbigstar%7ESolution%5C+1%5C+%22Use%5C+Invers%5C+Matriks%22%7D%7D%5C%5C%5C%5C2x-3y%3D4.......................%5B1%5D%5C%5C%7E%7Ex%2B3y%3D5.......................%5B2%5D%5C%5C%5C%5C%24Buat+model+matriksnya+%3A%24%5C%5C%5C%5C++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-3%5C%5C1%263%5Cend%7Barray%7D%5Cright%5D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%24Sehingga+%3A%24 "\bold{\underline{\bigstar~Solution\ 1\ \"Use\ Invers\ Matriks\"}}\\\\2x-3y=4.......................[1]\\~~x+3y=5.......................[2]\\\\$Buat model matriksnya :$\\\\ \left[\begin{array}{ccc}2&-3\\1&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]=\left[\begin{array}{ccc}4\\5\end{array}\right]\\\\$Sehingga :$")
![\displaystyle \left[\begin{array}{ccc}x\\y\end{array}\right]= \frac{1}{(2)(3)-(-3)(1)} \left[\begin{array}{ccc}3&3\\-1&2\end{array}\right] \left[\begin{array}{ccc}4\\5\end{array}\right]\\\\~~~~~~~~~= \frac{1}{6-(-3)} \left[\begin{array}{ccc}27\\6\end{array}\right]\\\\~~~~~~~~~= \frac{1}{9} \left[\begin{array}{ccc}27\\6\end{array}\right]\\\\~~~~~~~~~= \left[\begin{array}{ccc}3\\\frac{6}{9} \end{array}\right]\\\\$Jadi nilai dari :$\\\\\displaystyle x=3~~~~dan~~~~y= \frac{6}{9}= \frac{2}{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%3D+%5Cfrac%7B1%7D%7B%282%29%283%29-%28-3%29%281%29%7D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%263%5C%5C-1%262%5Cend%7Barray%7D%5Cright%5D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%7E%7E%7E%7E%7E%7E%7E%7E%7E%3D+%5Cfrac%7B1%7D%7B6-%28-3%29%7D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D27%5C%5C6%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%7E%7E%7E%7E%7E%7E%7E%7E%7E%3D+%5Cfrac%7B1%7D%7B9%7D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D27%5C%5C6%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%7E%7E%7E%7E%7E%7E%7E%7E%7E%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C%5Cfrac%7B6%7D%7B9%7D+%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%24Jadi+nilai+dari+%3A%24%5C%5C%5C%5C%5Cdisplaystyle+x%3D3%7E%7E%7E%7Edan%7E%7E%7E%7Ey%3D+%5Cfrac%7B6%7D%7B9%7D%3D+%5Cfrac%7B2%7D%7B3%7D++ "\displaystyle \left[\begin{array}{ccc}x\\y\end{array}\right]= \frac{1}{(2)(3)-(-3)(1)} \left[\begin{array}{ccc}3&3\\-1&2\end{array}\right] \left[\begin{array}{ccc}4\\5\end{array}\right]\\\\~~~~~~~~~= \frac{1}{6-(-3)} \left[\begin{array}{ccc}27\\6\end{array}\right]\\\\~~~~~~~~~= \frac{1}{9} \left[\begin{array}{ccc}27\\6\end{array}\right]\\\\~~~~~~~~~= \left[\begin{array}{ccc}3\\\frac{6}{9} \end{array}\right]\\\\$Jadi nilai dari :$\\\\\displaystyle x=3~~~~dan~~~~y= \frac{6}{9}= \frac{2}{3}")
![\bold{\underline{\bigstar~Solution\ 1\ "Use\ Determinan\ Matriks"}}\\\\2x-3y=4.......................[1]\\~~x+3y=5.......................[2]\\\\$Buat model matriksnya :$\\\\ \left[\begin{array}{ccc}2&-3\\1&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]=\left[\begin{array}{ccc}4\\5\end{array}\right]\\\\$Sehingga :$](https://tex.z-dn.net/?f=%5Cbold%7B%5Cunderline%7B%5Cbigstar%7ESolution%5C+1%5C+%22Use%5C+Determinan%5C+Matriks%22%7D%7D%5C%5C%5C%5C2x-3y%3D4.......................%5B1%5D%5C%5C%7E%7Ex%2B3y%3D5.......................%5B2%5D%5C%5C%5C%5C%24Buat+model+matriksnya+%3A%24%5C%5C%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-3%5C%5C1%263%5Cend%7Barray%7D%5Cright%5D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%24Sehingga+%3A%24 "\bold{\underline{\bigstar~Solution\ 1\ \"Use\ Determinan\ Matriks\"}}\\\\2x-3y=4.......................[1]\\~~x+3y=5.......................[2]\\\\$Buat model matriksnya :$\\\\ \left[\begin{array}{ccc}2&-3\\1&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]=\left[\begin{array}{ccc}4\\5\end{array}\right]\\\\$Sehingga :$")
![\left[\begin{array}{ccc}2&-3\\1&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]=\left[\begin{array}{ccc}4\\5\end{array}\right]\\\\ \Delta=\left|\begin{array}{ccc}2&-3\\1&3\end{array}\right|=(2)(3)-(-3)(1)=9\\\\$Untuk delta x :$\\\\\Delta x=\left|\begin{array}{ccc}4&-3\\5&3\end{array}\right|=(4)(3)-(-3)(5)=27\\\\$Untuk delta y :$\\\\\Delta y=\left|\begin{array}{ccc}2&4\\1&5\end{array}\right|=(2)(5)-(4)(1)=6\\\\\bold{Sehingga\ untuk\ nilai\ dari :}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-3%5C%5C1%263%5Cend%7Barray%7D%5Cright%5D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C5%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C+%5CDelta%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D2%26-3%5C%5C1%263%5Cend%7Barray%7D%5Cright%7C%3D%282%29%283%29-%28-3%29%281%29%3D9%5C%5C%5C%5C%24Untuk+delta+x+%3A%24%5C%5C%5C%5C%5CDelta+x%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D4%26-3%5C%5C5%263%5Cend%7Barray%7D%5Cright%7C%3D%284%29%283%29-%28-3%29%285%29%3D27%5C%5C%5C%5C%24Untuk+delta+y+%3A%24%5C%5C%5C%5C%5CDelta+y%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D2%264%5C%5C1%265%5Cend%7Barray%7D%5Cright%7C%3D%282%29%285%29-%284%29%281%29%3D6%5C%5C%5C%5C%5Cbold%7BSehingga%5C+untuk%5C+nilai%5C+dari+%3A%7D+ "\left[\begin{array}{ccc}2&-3\\1&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right]=\left[\begin{array}{ccc}4\\5\end{array}\right]\\\\ \Delta=\left|\begin{array}{ccc}2&-3\\1&3\end{array}\right|=(2)(3)-(-3)(1)=9\\\\$Untuk delta x :$\\\\\Delta x=\left|\begin{array}{ccc}4&-3\\5&3\end{array}\right|=(4)(3)-(-3)(5)=27\\\\$Untuk delta y :$\\\\\Delta y=\left|\begin{array}{ccc}2&4\\1&5\end{array}\right|=(2)(5)-(4)(1)=6\\\\\bold{Sehingga\ untuk\ nilai\ dari :}")
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