$\left\{ $$\begin{aligned} \overrightarrow{x} &= \dfrac{1}{3}\overrightarrow{a} + \dfrac{2}{3}\overrightarrow{b}\\ \overrightarrow{y} &= \dfrac{1}{3}\overrightarrow{a} - \dfrac{1}{3}\overrightarrow{b}\end{aligned}$$ \right.$

$\left\{ $$\begin{aligned} \overrightarrow{x} &= \dfrac{1}{3}\overrightarrow{a} + \dfrac{2}{3}\overrightarrow{b}\\ \overrightarrow{y} &= \dfrac{1}{3}\overrightarrow{a} - \dfrac{2}{3}\overrightarrow{b}\end{aligned}$$ \right.$

$\left\{ $$\begin{aligned} \overrightarrow{x} &= \dfrac{1}{3}\overrightarrow{a} + \dfrac{1}{3}\overrightarrow{b}\\ \overrightarrow{y} &= \dfrac{1}{3}\overrightarrow{a} - \dfrac{1}{3}\overrightarrow{b}\end{aligned}$$ \right.$

$\left\{ $$\begin{aligned} \overrightarrow{x} &= \dfrac{1}{3}\overrightarrow{a} + \dfrac{1}{3}\overrightarrow{b}\\ \overrightarrow{y} &= \dfrac{1}{3}\overrightarrow{a} - \dfrac{2}{3}\overrightarrow{b}\end{aligned}$$ \right.$

$\left\{ $$\begin{aligned} \overrightarrow{x} &= -\dfrac{2}{5}\overrightarrow{a} + \dfrac{12}{5}\overrightarrow{b} \\ \overrightarrow{y} &= \dfrac{4}{5}\overrightarrow{a} - \dfrac{4}{5}\overrightarrow{b}\end{aligned}$$ \right.$

$\left\{ $$\begin{aligned} \overrightarrow{x} &= \dfrac{2}{5}\overrightarrow{a} - \dfrac{12}{5}\overrightarrow{b}\\ \overrightarrow{y} &= \dfrac{4}{5}\overrightarrow{a} - \dfrac{4}{5}\overrightarrow{b}\end{aligned}$$ \right.$

$\left\{ $$\begin{aligned} \overrightarrow{x} &= \dfrac{2}{5}\overrightarrow{a} - \dfrac{12}{5}\overrightarrow{b} \\ \overrightarrow{y} &= -\dfrac{4}{5}\overrightarrow{a} + \dfrac{4}{5}\overrightarrow{b}\end{aligned}$$ \right.$

$\left\{ $$\begin{aligned} \overrightarrow{x} &= -\dfrac{2}{5}\overrightarrow{a} + \dfrac{12}{5}\overrightarrow{b}\\ \overrightarrow{y} &= -\dfrac{4}{5}\overrightarrow{a} + \dfrac{4}{5}\overrightarrow{b}\end{aligned}$$ \right.$

$\left\{ $$\begin{aligned} \overrightarrow{x} &= -\dfrac{1}{7}\overrightarrow{a} + \dfrac{13}{7}\overrightarrow{b}\\ \overrightarrow{y} &= \dfrac{5}{7}\overrightarrow{a} - \dfrac{2}{7}\overrightarrow{b}\end{aligned}$$ \right.$

$\left\{ $$\begin{aligned} \overrightarrow{x} &= -\dfrac{5}{7}\overrightarrow{a} - \dfrac{11}{7}\overrightarrow{b}\\ \overrightarrow{y} &= \dfrac{5}{7}\overrightarrow{a} - \dfrac{2}{7}\overrightarrow{b}\end{aligned}$$ \right.$

$\left\{ $$\begin{aligned} \overrightarrow{x} &= -\dfrac{5}{7}\overrightarrow{a} - \dfrac{11}{7}\overrightarrow{b}\\ \overrightarrow{y} &= \dfrac{3}{7}\overrightarrow{a} + \dfrac{6}{7}\overrightarrow{b}\end{aligned}$$ \right.$

$\left\{ $$\begin{aligned} \overrightarrow{x} &= -\dfrac{1}{7}\overrightarrow{a} + \dfrac{13}{7}\overrightarrow{b}\\ \overrightarrow{y} &= \dfrac{3}{7}\overrightarrow{a} + \dfrac{6}{7}\overrightarrow{b}\end{aligned}$$ \right.$