$$\begin{lgathered}\left \{ {{x^2+y^2=16} \atop {y=x+4 }} \right. \\ \\ x^2+(x+4)^2=16 \\ x^2+x^2+8x+16=16 \\ 2x^2+8x=0 \\ 2x(x+4)=0 \\ x_1=0 \\ x_2 = -4 \\ \\ y_1=0+4=4 \\ y_2=-4+4=0 \\ \\ OTBET: \ (0;4), \ (-4;0)\end{lgathered}$$
$$\begin{lgathered}\left \{ {{x^2+y^2=16} \atop {y=x+4 }} \right. \\ \\ x^2+(x+4)^2=16 \\ x^2+x^2+8x+16=16 \\ 2x^2+8x=0 \\ 2x(x+4)=0 \\ x_1=0 \\ x_2 = -4 \\ \\ y_1=0+4=4 \\ y_2=-4+4=0 \\ \\ OTBET: \ (0;4), \ (-4;0)\end{lgathered}$$