Question

Помогите решить системы, срочно!!!

Answer 1

1)
$\left \{ {{x+ 5y = 6} \atop {10xy + 24y^2 = - x^2}} \right. \\\\ \left \{ {{x =6 - 5y} \atop {10y(6-5y) + 24y^2 + (6-5y)^2= 0}} \right. \\\\ \left \{ {{x =6 - 5y} \atop {60y - 50y^2 + 24y^2 + 36 - 60y + 25y^2 = 0}} \right. \\\\ \left [ {{ \left \{ {{x = -24} \atop {y = 6}} \right.} \atop { \left \{ {{x = 36} \atop {y = -6}} \right.}} \right.$
Ответ: $(-24;6);(36;-6)$

2)
$\left \{ {{7x-2y=4} \atop {xy = 10}} \right. \\\\ \left \{ {{y = \frac{7x-4}{2} \atop} \atop {x(\frac{7x-4}{2}) = 10}} \right. \\\\ \left \{ {{y = \frac{7x-4}{2} \atop} \atop {7x^2 -4x - 20 = 0}} \right. \\\\ \left [ {{ \left \{ {{x = -\frac{10}{7} \atop} \atop {y = -7}} \right.} \atop { \left \{ {{x = 2 \atop} \atop {y = 5}} \right.}} \right.$
Ответ: $(-\frac{10}{7};-7);(2;5)$

3)
$\left \{ {{x^2 + y^2 = 73} \atop {x+y = 11}} \right. \\\\ \left \{ {{(11-y)^2 + y^2 = 73} \atop {x = 11 - y}} \right. \\\\ \left \{ {{121 - 22y + y^2 + y^2 = 73} \atop {x = 11 - y}} \right. \\\\ \left \{ {{2y^2 - 22y + 48 = 0 \ |:2 } \atop {x = 11 - y}} \right. \\\\ \left \{ {{y^2 - 11y + 24 = 0} \atop {x = 11 - y}} \right. \\\\ \left [ {{ \left \{ {{y = 3} \atop {x = 8}} \right.} \atop { \left \{ {{y = 8} \atop {x = 3}} \right.}} \right.$
Ответ: $(3;8);(8;3)$