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Đáp án: $\begin{array}{l}
a)x = \dfrac{{15}}{{13}};y = \dfrac{{20}}{{13}}\\
b)\,x = - \dfrac{7}{4};y = \dfrac{7}{2}\\
c)x = - 38;y = - 42\\
d)x = \dfrac{5}{2};y = \dfrac{3}{2}
\end{array}$
Giải thích các bước giải:
$\begin{array}{l}
a)\dfrac{x}{y} = \dfrac{3}{4}\\
\Leftrightarrow \dfrac{x}{3} = \dfrac{y}{4} = \dfrac{{2x}}{6} = \dfrac{{5y}}{{20}} = \dfrac{{2x + 5y}}{{6 + 20}} = \dfrac{{10}}{{26}} = \dfrac{5}{{13}}\\
\Leftrightarrow \left\{ \begin{array}{l}
x = \dfrac{5}{{13}}.3 = \dfrac{{15}}{{13}}\\
y = \dfrac{5}{{13}}.4 = \dfrac{{20}}{{13}}
\end{array} \right.\\
Vay\,x = \dfrac{{15}}{{13}};y = \dfrac{{20}}{{13}}\\
b)\dfrac{{2x}}{{3y}} = - \dfrac{1}{3}\\
\Leftrightarrow \dfrac{{2x}}{{ - 1}} = \dfrac{{3y}}{3} = \dfrac{{2x + 3y}}{{ - 1 + 3}} = \dfrac{7}{2}\\
\Leftrightarrow \left\{ \begin{array}{l}
2x = - \dfrac{7}{2}\\
3y = 3.\dfrac{7}{2}
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = \dfrac{{ - 7}}{4}\\
y = \dfrac{7}{2}
\end{array} \right.\\
Vay\,x = - \dfrac{7}{4};y = \dfrac{7}{2}\\
c)21.x = 19.y\\
\Leftrightarrow \dfrac{x}{{19}} = \dfrac{y}{{21}} = \dfrac{{x - y}}{{19 - 21}} = \dfrac{4}{{ - 2}} = - 2\\
\Leftrightarrow \left\{ \begin{array}{l}
x = - 2.19 = - 38\\
y = - 2.21 = - 42
\end{array} \right.\\
Vay\,x = - 38;y = - 42\\
d)\dfrac{x}{5} = \dfrac{y}{3} = k\left( {k > 0} \right)\\
\Leftrightarrow \left\{ \begin{array}{l}
x = 5k\\
y = 3k
\end{array} \right.\\
{x^2} - {y^2} = 4\\
\Leftrightarrow {\left( {5k} \right)^2} - {\left( {3k} \right)^2} = 4\\
\Leftrightarrow 25{k^2} - 9{k^2} = 4\\
\Leftrightarrow 16{k^2} = 4\\
\Leftrightarrow {k^2} = \dfrac{1}{4}\\
\Leftrightarrow k = \dfrac{1}{2}\left( {do:k > 0} \right)\\
\Leftrightarrow \left\{ \begin{array}{l}
x = 5k = \dfrac{5}{2}\\
y = 3k = \dfrac{3}{2}
\end{array} \right.
\end{array}$
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