At some point when solving you made a division error and found $\displaystyle{z}=\frac{{1}}{{2}}\usepackage{cmbright}\Huge\$ instead of $\displaystyle{z}={2}\usepackage{cmbright}\Huge\$ . You used the incorrect value to find the values of x and y in the second and third equations. However, the values do not make the first equation true, so they are not a solution.