1. Stating the problem: Solve the system of linear equations $$\begin{cases} -4p_1 + 3p_2 = -104 \\ 4p_1 - 4p_2 = -156 \end{cases}$$ 2. Add the two equations to eliminate $p_1$: $$(-4p_1 + 3p_2) + (4p_1 - 4p_2) = -104 + (-156)$$ which simplifies to $$-p_2 = -260$$ so $$p_2 = 260$$ 3. Substitute $p_2=260$ into the first equation to find $p_1$: $$-4p_1 + 3(260) = -104$$ $$-4p_1 + 780 = -104$$ $$-4p_1 = -104 - 780$$ $$-4p_1 = -884$$ $$p_1 = \frac{-884}{-4} = 221$$ 4. Final solution: $$\boxed{p_1 = 221, \quad p_2 = 260}$$