$10x-5y-2z=3 $ $x=\dfrac {1}{10} (3+5y+2z)$ $4x-10y+3z=-3$ $y=\dfrac {1}{10} (4x+3z+3)$ $x+6y+10z=-3$ $z=\dfrac {-1}{10}(x+6y+3)$ First iteration:   put y=z=0, $x_1 = \dfrac {3}{10}= 0.3$ $y_1=\dfrac {1}{10} (4\times 0.3+3)=0.42$ $z_1=\dfrac {-1}{10}(0.3+6\times 0.42+3)=-0.582$ Second iteration: $x_2=\dfrac {1}{10} (3+5(0.42)+2(-0.582))=0.3936$ $y_2 = \dfrac {1}{10} (4 (0.3936)+3(-0.582)+3)=0.28284$ $z_2 = \dfrac {-1}{10} (0.3936+6(0.28284)+3) \approx -0.509$ Third iteration: $x_3=\dfrac {1}{10} (3+5(0.28284)+2(-0.509)) \approx 0.334$ $y_3 = \dfrac {1}{10} (4 (0.33962)+3(-0.509)+3) \approx 0.283$ $z_3= \dfrac {-1}{10} (0.334+6(0.283)+3) \approx -0.503$

Hence the approximate values of (x,y,z) are (0334, 0.283, -0.503)