$$\frac{2}{3}\cdot(-8)+\frac{1}{3}\cdot(-2) = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{2}{3}\cdot(-8)+\frac{1}{3}\cdot(-2) &= 0&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3 \cdot \frac{2}{3}\cdot(-8)+3\frac{1}{3}\cdot(-2) &= 3\cdot0&& \text{cancel out the denominators} \\[1 em]-16+(-2) &= 0&& \text{simplify left side} \\[1 em]-16-2 &= 0&& \\[1 em]-18 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ -18 = 0 } $ is FALSE, we conclude that the equation has no solution.
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