Đáp án:
a) x và y tỉ lệ thuận nên:
$\begin{array}{l}
\dfrac{{{x_1}}}{{{x_2}}} = \dfrac{{{y_1}}}{{{y_2}}}\\
a){x_1} = 1\dfrac{4}{7} = \dfrac{{11}}{7}\\
{y_1} = 5\dfrac{1}{2} = \dfrac{{11}}{2}\\
{y_2} = - 2\dfrac{1}{3} = \dfrac{{ - 7}}{3}\\
Do:\dfrac{{{x_1}}}{{{x_2}}} = \dfrac{{{y_1}}}{{{y_2}}}\\
\Rightarrow {x_2} = \dfrac{{{x_1}.{y_2}}}{{{y_1}}} = \dfrac{{\dfrac{{11}}{7}.\dfrac{{ - 7}}{3}}}{{\dfrac{{11}}{2}}} = \dfrac{{\dfrac{{ - 11}}{3}}}{{\dfrac{{11}}{2}}} = - \dfrac{2}{3}\\
Vậy\,{x_2} = \dfrac{{ - 2}}{3}\\
b)\dfrac{{{x_1}}}{{{x_2}}} = \dfrac{{{y_1}}}{{{y_2}}}\\
= \dfrac{{3{x_1}}}{{3{x_2}}} = \dfrac{{2{y_1}}}{{2{y_2}}} = \dfrac{{3{x_1} + 2{y_1}}}{{3.6 + 2.3}} = \dfrac{{20}}{{24}} = \dfrac{5}{6}\\
\Rightarrow \left\{ \begin{array}{l}
{x_1} = \dfrac{5}{6}.{x_2} = \dfrac{5}{6}.6 = 5\\
{y_1} = \dfrac{5}{6}.{y_2} = \dfrac{5}{6}.3 = \dfrac{5}{2}
\end{array} \right.\\
Vậy\,{x_1} = 5;{y_1} = \dfrac{5}{2}
\end{array}$
