Giải thích các bước giải:
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\begin{array}{l}
a,\\
\dfrac{x}{{16}} = \dfrac{y}{{18}} = \dfrac{{x + y}}{{16 + 18}} = \dfrac{{68}}{{34}} = 2\\
\Rightarrow \left\{ \begin{array}{l}
\dfrac{x}{{16}} = 2\\
\dfrac{y}{{18}} = 2
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = 32\\
y = 36
\end{array} \right.\\
b,\\
\dfrac{x}{3} = \dfrac{y}{4} = \dfrac{{x + y}}{{3 + 4}} = \dfrac{{28}}{7} = 4\\
\Rightarrow \left\{ \begin{array}{l}
\dfrac{x}{3} = 4\\
\dfrac{y}{4} = 4
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x = 12\\
y = 16
\end{array} \right.\\
c,\\
\dfrac{x}{{ - 2}} = \dfrac{y}{7} = \dfrac{{x + y}}{{\left( { - 2} \right) + 7}} = \dfrac{{105}}{5} = 21\\
\Rightarrow \left\{ \begin{array}{l}
\dfrac{x}{{ - 2}} = 21\\
\dfrac{y}{7} = 21
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = - 42\\
y = 147
\end{array} \right.\\
d,\\
\dfrac{x}{{ - 12}} = \dfrac{y}{{ - 17}} = \dfrac{{x - y}}{{\left( { - 12} \right) - \left( { - 17} \right)}} = \dfrac{8}{5}\\
\Rightarrow \left\{ \begin{array}{l}
\dfrac{x}{{ - 12}} = \dfrac{8}{5}\\
\dfrac{y}{{ - 17}} = \dfrac{8}{5}
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = - \dfrac{{96}}{5}\\
y = - \dfrac{{136}}{5}
\end{array} \right.
\end{array}\)
