$\begin{array}{l}\\ 6.&\textrm{SPL berikut memiliki selesaian}....\\ &\begin{cases} 2x-7y & =-19 \\ 3x-y & =0 \end{cases}\\ &\begin{array}{llllllll}\\ \textrm{a}.&x=-3\quad \textrm{dan}\quad y=-1\\ \textrm{b}.&x=3\quad \textrm{dan}\quad y=1\\ \textrm{c}.&x=1\quad \textrm{dan}\quad y=3\\ \textrm{d}.&x=-3\quad \textrm{dan}\quad y=1\\ \textrm{e}.&x=1\quad \textrm{dan}\quad y=-3 \end{array}\\\\ &\textbf{Jawab}:\quad \textbf{c}\\ &\textrm{Dengan metode eliminasi Gauss didapatkan}\\ &\left[ \begin{array}{cc|c} 2&-7&-19\\ 3&-1&0 \end{array} \right]\quad\bullet R_{\displaystyle 2}\longleftarrow 2R_{\displaystyle 2}-3R_{\displaystyle 1}\\ &=2(3,-1|0)-3(2,-7|-19)=(0,19|57)\\ &\textrm{Sehingga diperoleh}\\ &\left[ \begin{array}{cc|c} 2&-7&-19\\ 0&19&57 \end{array} \right]\\ &\textrm{sehingga}\quad y=\displaystyle \frac{57}{19}=3,\quad \textrm{maka}\quad x=1 \end{array}$.
$\begin{array}{l}\\ 7.&\textrm{SPL berikut memiliki selesaian}....\\ &\begin{cases} 4x-3y & =14 \\ -x+2y & =-1 \end{cases}\\ &\begin{array}{llllllll}\\ \textrm{a}.&x=2\quad \textrm{dan}\quad y=5\\ \textrm{b}.&x=5\quad \textrm{dan}\quad y=-2\\ \textrm{c}.&x=5\quad \textrm{dan}\quad y=2\\ \textrm{d}.&x=-5\quad \textrm{dan}\quad y=-2\\ \textrm{e}.&x=-2\quad \textrm{dan}\quad y=-5 \end{array}\\\\ &\textbf{Jawab}:\quad \textbf{c}\\ &\textrm{Dengan metode eliminasi Gauss didapatkan}\\ &\left[ \begin{array}{cc|c} 4&-3&14\\ -1&2&-1 \end{array} \right]\quad\bullet R_{\displaystyle 2}\longleftarrow R_{\displaystyle 2}+\displaystyle \frac{1}{4}R_{\displaystyle 1}\\ &=(-1,2|-1)+\displaystyle \frac{1}{4}(4,-3|14)=(0,\displaystyle \frac{5}{4}|\displaystyle \frac{10}{4})\\ &\textrm{Sehingga diperoleh}\\ &\left[ \begin{array}{cc|c} 4&-3&14\\ 0&\displaystyle \frac{5}{4}&\displaystyle \frac{10}{4} \end{array} \right]\\ &\textrm{sehingga}\quad y=\displaystyle \frac{\displaystyle \frac{10}{4}}{\displaystyle \frac{5}{4}}=2,\quad \textrm{maka}\quad x=1 \end{array}$.
$\begin{array}{l}\\ 8.&\textrm{SPL berikut memiliki selesaian}....\\ &\begin{cases} 8x+3y & =37 \\ 4x+y & =15 \end{cases}\\ &\begin{array}{llllllll}\\ \textrm{a}.&x=2\quad \textrm{dan}\quad y=7\\ \textrm{b}.&x=2\quad \textrm{dan}\quad y=-7\\ \textrm{c}.&x=7\quad \textrm{dan}\quad y=-2\\ \textrm{d}.&x=7\quad \textrm{dan}\quad y=2\\ \textrm{e}.&x=-2\quad \textrm{dan}\quad y=-7 \end{array}\\\\ &\textbf{Jawab}:\quad \textbf{a}\\ &\textrm{Dengan metode eliminasi Gauss didapatkan}\\ &\left[ \begin{array}{cc|c} 8&3&37\\ 4&1&15 \end{array} \right]\quad\bullet R_{\displaystyle 2}\longleftarrow R_{\displaystyle 2}-\displaystyle \frac{1}{2}R_{\displaystyle 1}\\ &=(4,1|15)-\displaystyle \frac{1}{2}(8,3|37)=(0,-\displaystyle \frac{1}{2}|-\displaystyle \frac{7}{2})\\ &\textrm{Sehingga diperoleh}\\ &\left[ \begin{array}{cc|c} 8&3&37\\ 0&-\displaystyle \frac{1}{2}&-\displaystyle \frac{7}{2} \end{array} \right]\\ &\textrm{sehingga}\quad y=\displaystyle \frac{-\displaystyle \frac{7}{2}}{-\displaystyle \frac{2}{2}}=7,\quad \textrm{maka}\quad x=2 \end{array}$.
$\begin{array}{l}\\ 9.&\textrm{SPL berikut memiliki selesaian}....\\ &\begin{cases} 4x+2y+3z & =0 \\ 2x+3y+5z & =9\\ 3x+y+7z & =9 \end{cases}\\ &\begin{array}{llllllll}\\ \textrm{a}.&x=-2,\quad y=1\quad \textrm{dan}\quad z=2\\ \textrm{b}.&x=2,\quad y=1\quad \textrm{dan}\quad z=2\\ \textrm{c}.&x=-2,\quad y=-1\quad \textrm{dan}\quad z=-2\\ \textrm{d}.&x=-2,\quad y=1\quad \textrm{dan}\quad z=-2\\ \textrm{e}.&x=-2,\quad y=-1\quad \textrm{dan}\quad z=2 \end{array}\\\\ &\textbf{Jawab}:\quad \textbf{a}\\ &\textrm{Dengan metode eliminasi Gauss didapatkan}\\ &\left[ \begin{array}{ccc|c} 4&2&3&0\\ 2&3&5&9\\ 3&1&7&9 \end{array} \right]\quad\begin{matrix} \bullet R_{\displaystyle 2}\longleftarrow 2R_{\displaystyle 2}-R_{\displaystyle 1}\: .\\ \bullet R_{\displaystyle 3}\longleftarrow 4R_{\displaystyle 3}-3R_{\displaystyle 1} \end{matrix}\\ &=2(2,3,5|9)-(4,2,3|0)=(0,4,7|18)\quad \textrm{dan}\\ &=4(2,3,5|9)-3(4,2,3|0)=(0,-2,19|36)\\ &\textrm{Sehingga diperoleh}\\ &\left[ \begin{array}{ccc|c} 4&2&3&0\\ 0&4&7&18\\ 0&-2&19&36 \end{array} \right]\quad \bullet R_{\displaystyle 3}\longleftarrow 2R_{\displaystyle 3}+R_{\displaystyle 2}\\ &=2(0,-2,19|36)+(0,4,7|18)=(0,0,45|90)\\ &\textrm{sehingga}\quad z=\displaystyle \frac{90}{45}=2,\quad \textrm{maka}\quad y=1,\:\: x=-2 \end{array}$.
$\begin{array}{l}\\ 10.&\textrm{SPL berikut memiliki selesaian}....\\ &\begin{cases} 7x+2y+z & =-40 \\ 2x+7y+4z & =45\\ 5x-4y+6z & =8 \end{cases}\\ &\begin{array}{llllllll}\\ \textrm{a}.&x=-8,\quad y=-3\quad \textrm{dan}\quad z=10\\ \textrm{b}.&x=-8,\quad y=3\quad \textrm{dan}\quad z=10\\ \textrm{c}.&x=-8,\quad y=3\quad \textrm{dan}\quad z=-10\\ \textrm{d}.&x=8,\quad y=3\quad \textrm{dan}\quad z=10\\ \textrm{e}.&x=8,\quad y=-3\quad \textrm{dan}\quad z=10 \end{array}\\\\ &\textbf{Jawab}:\quad \textbf{b}\\ &\textrm{Dengan metode eliminasi Gauss didapatkan}\\ &\left[ \begin{array}{ccc|c} 7&2&1&-40\\ 2&7&4&45\\ 5&-4&6&8 \end{array} \right]\quad\begin{matrix}\bullet R_{\displaystyle 2}\longleftarrow 7R_{\displaystyle 2}-2R_{\displaystyle 1}\\ \bullet R_{\displaystyle 3}\longleftarrow 7R_{\displaystyle 3}-5R_{\displaystyle 1}\end{matrix}\\ &=7(2,7,4|45)-2(7,2,1|-40)=(0,45,26|395)\:\:\textrm{dan}\\ &=7(5,-4,6|8)-5(7,2,1|-40)=(0,-38,37|256)\\ &\textrm{Sehingga diperoleh}\\ &\left[ \begin{array}{ccc|c} 7&2&1&-40\\ 0&45&26&395\\ 0&-38&37&256 \end{array} \right]\quad \bullet R_{\displaystyle 3}\longleftarrow \displaystyle \frac{1}{45}R_{\displaystyle 3}+\displaystyle \frac{1}{38}R_{\displaystyle 2}\\ &=\displaystyle \frac{1}{45}(0,-38,37|256)+\displaystyle \frac{1}{38}(0,45,26|395)=(0,0,\displaystyle \frac{2653}{1710}|\displaystyle \frac{26530}{1710})\\ &\textrm{sehingga}\quad z=\displaystyle \frac{\displaystyle \frac{226530}{1710}}{\displaystyle \frac{2653}{1710}}=10,\quad \textrm{maka}\quad y=3,\:\: x=-8 \end{array}$.
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