Đáp án:
Áp dụng tính chất dãy tỉ số bằng nhau:
$\begin{array}{l}
13)\dfrac{{x - 1}}{2} = \dfrac{{y + 2}}{3} = \dfrac{{x - 1 + y + 2}}{{2 + 3}} = \dfrac{{4 + 1}}{5} = 1\\
\Rightarrow \left\{ \begin{array}{l}
x - 1 = 2\\
y + 2 = 3
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 3\\
y = 1
\end{array} \right.\\
\text{Vậy}\,x = 3;y = 1\\
14)\\
\dfrac{{x + 1}}{2} = \dfrac{{y + 3}}{4} = \dfrac{{2\left( {x + 1} \right)}}{4} = \dfrac{{3\left( {y + 3} \right)}}{{12}}\\
= \dfrac{{2x + 2 + 3y + 9}}{{4 + 12}} = \dfrac{{5 + 2 + 9}}{{16}} = 1\\
\Rightarrow \left\{ \begin{array}{l}
x + 1 = 2\\
y + 3 = 4
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 1\\
y = 1
\end{array} \right.\\
\text{Vậy}\,x = 1;y = 1\\
15)\\
\dfrac{{2 - x}}{3} = \dfrac{{3 - y}}{2} = \dfrac{{5\left( {2 - x} \right)}}{{5.3}} = \dfrac{{3.\left( {3 - y} \right)}}{{3.2}}\\
= \dfrac{{10 - 5x}}{{15}} = \dfrac{{9 - 3y}}{6}\\
= \dfrac{{9 - 3y - \left( {10 - 5x} \right)}}{{6 - 15}}\\
= \dfrac{{9 - 10 + 5x - 3y}}{{ - 9}}\\
= \dfrac{{ - 1 + \left( { - 8} \right)}}{{ - 9}} = 1\\
\Rightarrow \left\{ \begin{array}{l}
2 - x = 3\\
3 - y = 2
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x = - 1\\
y = 1
\end{array} \right.\\
\text{Vậy}\,x = - 1;y = 1
\end{array}$
