Mesh analysis with current sources
I get the following equations

$$\begin{align} i_1R_1 - i_2R_2-i_3R_3&amp;=0\\
i_1+i_2&amp;=I_s\\
i_3R_3+i_4R_4&amp;=V_s\\
i_1+i_3-i_4&amp;=0
\end{align}$$

With the given values this results in

$$i_1=1.007353\;A\\
i_2=0.992647\;A\\
i_3=0.051471\;A\\
i_4=1.058824\;A$$

And the current through the voltage source is simply \$i_2-i_3\$.

EDIT:

Your equations on paper are correct, but you made a mistake setting up your matrix. It should be 

\begin{pmatrix} R_1 + R_2 + R_3 &amp; -R_2 &amp; -R_3 &amp; 0 \\ 0 &amp; 1 &amp; 0 &amp; I_s \\ -R_3 &amp; 0 &amp; R_3+R_4 &amp; V_s \end{pmatrix}

Solving this system gives the mesh currents:

$$i_{m1}=1.0074\;A\\
i_{m2}=2.0000\;A\\
i_{m3}=1.0588\;A$$

Note that the mesh currents are generally not equal to the currents in the diagram. The actual currents are given by

$$\begin{align}i_1&amp;=i_{m1}\\
i_2&amp;=i_{m2}-i_{m1}\\
i_3&amp;=i_{m3}-i_{m1}\\
i_4&amp;=i_{m3}\end{align}$$