Diberikan persamaan \(\dfrac {x - 2}{3} + \dfrac {y + 1}{6} = 2\) dan \(\dfrac {x + 3}{4} + \dfrac {2y - 1}{2} = 1 \), maka nilai \( \dfrac {1}{x + y} = \dotso\)
Jawab: D
\begin{equation*}
\begin{split}
\frac {x - 2}{3} + \frac {y + 1}{6} & = 2 \quad {\color {blue} \times \: 6} \\\\
2(x - 2) + y + 1 & = 12 \\\\
2x - 4 + y + 1 &= 12 \\\\
2x + y & = 15 \quad {\color {blue} \dotso \: (1)} \\\\
\end{split}
\end{equation*}
\begin{equation*}
\begin{split}
\dfrac {x + 3}{4} + \dfrac {2y - 1}{2} & = 1 \quad {\color {blue} \times \: 4} \\\\
x + 3 + 2(2y - 1) & = 4 \\\\
x + 3 + 4y - 2 & = 4 \\\\
x + 4y & = 3 \quad {\color {blue} \dotso \: (2)} \\\\
\end{split}
\end{equation*}
Eliminasi persamaan (1) dan (2)
\begin{equation*}
\begin{array}{lllllllll}
2x & + & y & = 15 & | \: \times 1 \: | & 2x & + & y & = 15 \\\\
x & + & 4y & = 3 & | \: \times 2 \: | & 2x & + & 8y & = 6 \quad (-) \\\\
\hline \\
&&&&&&& -7y & = 9 \\\\
&&&&&&& y & = - \dfrac 97
\end{array}
\end{equation*}
Substitusi \(y = - \dfrac 97\) ke persamaan (1)
\begin{equation*}
\begin{split}
2x + y & = 15 \\\\
2x - \frac 97 & = 15 \quad {\color {blue} \times \: 7} \\\\
14x - 9 & = 105 \\\\
14x & = 114 \\\\
x & = \frac {57}{7}
\end{split}
\end{equation*}
Nilai dari \(\dfrac {1}{x + y}\)
\begin{equation*}
\begin{split}
& \frac {1}{x + y} \\\\
& \frac {1}{\frac {57}{7} - \frac 97} \\\\
& \frac {1}{\frac {48}{7}} \\\\
& \frac {7}{48} \
\end{split}
\end{equation*}
