I have the following circuit, and I have to find Vo
:
I solved it in this way:
$$ \\ \begin{cases} \frac{v_1 - 40}{1} + \frac{v_1 - v_0}{2} + 5 = 0 \\ \frac{v_1 - v_0}{2} + 5 = \frac{v_0 - (-20)}{8} + \frac{v_0}{4} \end{cases} \\ \begin{cases} 2v_1 - 80 + v_1 - v_0 + 10 = 0 \\ 4v_1 - 4v_0 + 40 - v_0 -20 - 2v_0 = 0 \end{cases} \\ \begin{cases} 3v_1 - v_0 = 70 \\ 4v_1 - 7v_0 = - 20 \end{cases} \\ v_0 = 3v_1 - 70 \\ 4v_1 - 21v_1 + 490 = -20 \\ 17v_1 = 510 \\ v_1 = \frac{510}{17} = 30 V \\ v_0 = 3v_1 - 70 = 20 \\ \begin{cases} v_1 = 30 V \\ v_0 = 20 V \end{cases} $$
But the solution is this:
I think that the error is in the solution, because in the first equation there is:
$$ \frac{40 - v_0}{1} $$
instead of:
$$ \frac{40 - v_1}{1} $$
but I'm not sure. Is my solution right or wrong?