Nodal analysis with dependent voltage source
Writing nodal equation at ground node,
$$-7 =\frac{V_1}{10} + \frac{V_2}{5} + \frac{V_2}{2}$$
$$or,\ \mathbf{0.1V_1 + 0.7V_2 = -7}$$
Writing nodal equation at \$V_1\$ correctly will also produce the same equation. You actually missed the term \$0.7V_2\$ in it. 

Now,
$$V_2 = V_1+6I_x$$
but, $$I_x = -0.1V_1$$ 
then,
$$V_2 = 0.4V_1$$ 
$$\mathbf{0.4V_1 - V_2 = 0}$$

Writing these equations in matrix format,
$$
\left[ \begin{array}{cc}
0.4 &amp; -1 \\
0.1 &amp; 0.7\end{array} \right]\left[ \begin{array}{c}
V_1 \\
V_2\end{array} \right]=\left[ \begin{array}{c}
0 \\
-7\end{array} \right]
$$

I am getting an extra -1. Correct me if I am wrong.