System of inequalities with 3 variables I have a system of inequalities:
\begin{array}{c}
a-b+c>0 \\ 
a+b+c<4 \\ 
9a-3b+c<-5
\end{array}
Wolfram|Alpha says that \begin{array}{c} a < -\frac {1}{8} \end{array}
But how can I solve this system of inequalities for this answer?

Solving the system
$$
\cases{
a-b+c=s_1^2\\
a+b+c-4=-s_2^2\\
9a-3b+c+5=-s_3^2
}
$$
we obtain the solutions
$$
\cases{
a=-\frac 18-\frac 18(2s_1^2+s_2^2+s_3^2)\\
b=2-\frac 12(s_1^2+s_2^2)\\
c=\frac 18(17+6s_1^2-3s_2^2+s_3^3)
}
$$
so we can conclude easily that
$$
a < -\frac 18, \ \ b < 2
$$
