How do I calculate i, i1, i2 and v2?
Well, we are trying to analyze the following circuit:







simulate this circuit &ndash; Schematic created using CircuitLab

Using KCL, we can write:

$$\text{I}_1=\text{I}_2+\text{I}_3\tag1$$

Using KVL, we can write:

$$
\begin{cases}
\text{I}_1=\frac{\text{V}_\text{a}-\text{V}_1}{\text{R}_1}\\
\\
\text{I}_2=\frac{\text{V}_2}{\text{R}_2}\\
\\
\text{I}_3=\frac{\text{V}_1}{\text{R}_3}\\
\\
\text{V}_\text{x}=\text{V}_1-\text{V}_2=\alpha\text{I}_1
\end{cases}\tag2
$$

Using some Mathematica code:

FullSimplify[
 Solve[{I1 == I2 + I3, I1 == (Va - V1)/R1, I2 == V2/R2, I3 == V1/R3, 
   Vx == V1 - V2 == α*I1}, {I1, I2, I3, V1, V2, Vx}]]


Using Your values we get:

FullSimplify[
 Solve[{I1 == I2 + I3, I1 == (10 - V1)/20, I2 == V2/25, I3 == V1/50, 
   Vx == V1 - V2 == 5*I1}, {I1, I2, I3, V1, V2, Vx}]]


Which gives:

{{I1 -&gt; 1/4, I2 -&gt; 3/20, I3 -&gt; 1/10, V1 -&gt; 5, V2 -&gt; 15/4, Vx -&gt; 5/4}}


Which approximate to:

{{I1 -&gt; 0.25, I2 -&gt; 0.15, I3 -&gt; 0.1, V1 -&gt; 5., V2 -&gt; 3.75, 
  Vx -&gt; 1.25}}