By solving the following system of equations:
we obtain that \(\frac{x}{y}\) equals to:
-
\(\cfrac{4}{3}\)
-
\(\cfrac{3}{4}\)
-
\(\cfrac{1}{12}\)
-
\(-\cfrac{16}{5}\)
-
\(-\cfrac{26}{23}\)
Try to solve it before checking the answer.
-
\(\cfrac{4}{3}\)
Multiplying both equations by \(x\):
\(
2 – \cfrac{x}{y} = 2x
\hspace{4em} \boldsymbol{(2)}
\)
\(
1 + 2 \cfrac{x}{y} = 11x
\hspace{4em} \boldsymbol{(3)}
\)
Multiplying the equation (2) by -11, and the equation (3) by 2:
\(
-22 + 11 \cfrac{x}{y} = -22x
\hspace{4em} \boldsymbol{(4)}
\)
\(
2 + 4 \cfrac{x}{y} = 22x
\hspace{4em} \boldsymbol{(5)}
\)
Adding the above equations:
\begin{aligned}
-20 + 15 \frac{x}{y} = 0
&\Rightarrow
15 \frac{x}{y} = 20
\\[.5em]
&\Rightarrow
\frac{x}{y} = \frac{20}{15}
\\[.5em]
&\Rightarrow
\frac{x}{y} = \boldsymbol{\frac{4}{3}}
\end{aligned}
\]