[tex]\displaystyle \left \{ {{2p+z=0} \atop {-z+3p=1}} \right. \\\\\left \{ {{2p+z=0} \atop {3p-z=1}} \right. \\\\(2p+z)+(3p-z)=1\\5p=1\\\\p=\frac{1}{5}\\ \\2p+z=0\\\\z=-\frac{2}{5}\\ \\(p,z)=(\frac{1}{5},-\frac{2}{5})[/tex]