How to derive this Hicksian Demand?
Since in this case, both utility function and the budget line are perfect substitutes and thus you can't equate the Marginal Rate of Substitution to the price ratio.

This problem can be solved this way,

$$\min_{x,y} \quad  3x+3y\\
    \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \textrm{s.t.} \quad  2x+5y=10\\$$

or

$$\min_{x,y} \quad  x+y\\
    \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  \ \textrm{s.t.} \quad  2x+5y=10\\$$

Here,
     $$MRS=\frac{MU_{x}}{MU_{y}}=\frac{2}{5}&lt;1=\frac{P_{x}}{P_{y}}$$ 
or,  $$\frac{MU_{x}}{P_{x}}=2 &lt; 5 = \frac{MU_{y}}{P_{y}}$$ 

Therefore the expenditure is minimum when the consumer spends his entire income on good y, that is $(x,y)=(0,2)$ is the bundle that minimizes the expenditure given the utility $u(x,y)=2x+5y=10$. This is depicted in the figure below: