Substitution effect when price of both goods change by the same percentage
Consider the budget line with 2 goods:
\begin{equation}
p_xx+p_yy=m
\quad\text{or}\quad 
y=\frac{m}{p_y}-\frac{p_x}{p_y}x,
\end{equation}
where the relative price is $\frac{p_x}{p_y}$. 

Suppose now both goods become $10\%$ more expensive (e.g. due to a $10\%$ tax on them). Then the budget line becomes
\begin{equation}
1.1p_xx+1.1p_yy=m
\quad\Leftrightarrow\quad 
p_xx+p_yy=\frac{m}{1.1}
\quad\text{or}\quad 
y=\frac{m}{1.1p_y}-\frac{1.1p_x}{1.1p_y}x=\frac{m}{1.1p_y}-\frac{p_x}{p_y}x
\end{equation}
where the relative price is still $\frac{p_x}{p_y}$. From the equations, we see that a uniform percentage change in prices produces a pure income effect ($m$ drops to $m/1.1$), but no substitution effect, since the relative price remain the same after the change.