Question

Реши систему уравнений:

Answer 1

Объяснение:

$\left \{ {{\frac{1}{4x-7y}+x=2 } \atop {\frac{x}{4x-7y}=-8 }} \right.$

$\left \{{\frac{1}{4x-7y}+x=2} \atop {x=-8(4x-7y)|:(-8)} \right.$

$\left \{ {{\frac{1}{4x-7y}+x=2 } \atop {-\frac{x}{8}=(4x-7y) }} \right.$

$\left \{ {{-\frac{8}{x}+x=2|*(x) } \atop {-\frac{x}{8}=(4x-7y) }} \right.$

$\left \{ {{-8+x^{2}=2x } \atop {-\frac{x}{8}=(4x-7y) } \right.; x^{2} -2x-8=0; (x+2)(x-4)=0; {x_{1}=-2; x_{2} =4}$

$\left \{ {{x_{1} =-2} \atop {\frac{1}{4}=-8-7y|*4 }} \right; 1=-32-28y; 33=-28y; y=-\frac{33}{28}; \boxed{y_{1} =-1\frac{5}{28}}$

$\boxed{\left \{ {{x_{1}=-2 } \atop {y_{1}=-4\frac{5}{7} }} \right.}$

$\left \{ {{x_{2}=4 } \atop {-\frac{1}{2}=16-7y|*2 }} \right.; -1=32-14y;-33=-14y; y=\frac{33}{14}; \boxed{y_{2}=2\frac{5}{14}}$

$\boxed{\left \{ {{x_{2}=4 } \atop {y_{2} =2\frac{5}{14} }} \right. }$