The value of current i₁ in the given circuit is

$\mathrm{i}={\mathrm{i}}_1+{\mathrm{i}}_2\dots \left(1\right);$

$-{\mathrm{i}}_1\mathrm{r}-{\mathrm{i}}_3\mathrm{r}+2{\mathrm{i}}_2\mathrm{r}=0$

$-{\mathrm{i}}_1-{\mathrm{i}}_3+2{\mathrm{i}}_2=0\dots \text{ (2) }$

$-\left({\mathrm{i}}_1-{\mathrm{i}}_3\right)2\mathrm{r}+\left({\mathrm{i}}_2+{\mathrm{i}}_3\right)\mathrm{r}+{\mathrm{i}}_3\mathrm{r}=0$

$-2{\mathrm{i}}_1+4{\mathrm{i}}_3+{\mathrm{i}}_2=0...\left(3\right)$; 

Solving  (1) (2) & (3) gives 

${\mathrm{i}}_1=\frac{3\mathrm{i}}{5}$