Question

сколько решений имеет система
${x}^{2} + {y}^{2} = 16 \\ y - x = 4$

Answer 1

$\left \{ {{y=x+4} \atop {x^{2}+(x+4)^{2}}=16 } \right. \\\\\left \{ {{y=x+4} \atop {x^{2}+ x^{2}+8x+16}=16} \right.\\\\\left \{ {{y=x+4} \atop {2x^{2}+8x=0} } \right.\\\\\left \{ {{y=x+4} \atop {2x(x+4)=0}} \right.\\\\\left \{ {{x_{1}=0} \atop {y_{1}=4} } \right. \\\\\left \{ {{x_{2}=-4} \atop {y_{2}=0 } \right.$

Ответ :  два решения (0 ; 4) , ( - 4 , 0)