How to solve this equation if we can't use Chinese remainder theorem. Let consider:
$$\begin{cases}6x \equiv 2 \mod 8\\ 5x \equiv 5\mod 6 \end{cases}$$
We can't use Chinese remainder theorem because $\gcd(8,6) = 2 > 1$
Help me.

$$
\begin{array}{l}
 \left\{ \begin{array}{l}
 6x \equiv 2\left[ 8 \right] \\ 
 5x \equiv 5\left[ 6 \right] \\ 
 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
 3x \equiv 1\left[ 4 \right] \\ 
 x \equiv 1\left[ 6 \right] \\ 
 \end{array} \right. \\ 
  \Rightarrow \left\{ \begin{array}{l}
 x \equiv  - 1\left[ 4 \right] \\ 
 x \equiv 1\left[ 6 \right] \\ 
 \end{array} \right. \Rightarrow \left\{ \begin{array}{l}
 x \equiv 3\left[ 4 \right] \\ 
 x \equiv 1\left[ 6 \right] \\ 
 \end{array} \right. \\ 
 4k + 3 = 6m + 1 \Leftrightarrow 1 = 3m - 2k \\ 
 \end{array}
$$
