Question

{х²+у²=101
х+у=11
система уравнений​

Answer 1

{х^2+у^2=101, {х+у=11 x=11-y (11-y)^2+y^2=101 121-22y+y^2+y^2-101=0 2y^2-22y+20=0 y^2-11y+10=0 y1=1 x1=10 y2=10 x2=1

Answer 2

Ответ:

$\left \{ {{ {x}^{2} + {y}^{2} = 101 } \atop {x + y = 11}} \right . \: = > \left \{ {{ {x}^{2} + {y}^{2} = 101 } \atop {x = 11 - y}} \right .$

Подставляем вторую строчку в первую

${(11 - y)}^{2} + {y}^{2} = 101 \\ 121 - 22y + {y}^{2} + {y}^{2} = 101 \\ 2 {y}^{2} - 22y + 121 - 101 = 0 \\ 2 {y}^{2} - 22y + 20 = 0 \\ {y}^{2} - 11y + 10 = 0$

$y_{1} = 1 \: \: \: \: \: \: \: \: \: \: \: y_{2} = 10$

Находим x:

$x = 11 - y \\ x_{1} = 11 - 1 = 10 \\ x_{2} = 11 - 10 = 1$

$(x_{1};y_{1}) = (10;1) \\ (x_{2};y_{2}) = (1;10)$