Question

Объясните, как решать системы уравнений методом введения новой переменной. например: 1/x+5/y=3.5 3/x-2/y=2

Answer 1

$\left \{ {{ \frac{1}{x} + \frac{5}{y} =3,5} \atop { \frac{3}{x} - \frac{2}{y}=2 }} \right. \left \{ {{ \frac{1}{x} + 5*\frac{1}{y} =3,5} \atop { 3*\frac{1}{x} - 2*\frac{1}{y}=2 }} \right.$

$\frac{1}{x} =a ; \frac{1}{y} =b$

$\left \{ {{a+5b=3,5} \atop {3a-2b=2}} \right. \left \{ {{a=3,5-5b} \atop {3(3,5-5b)-2b=2}} \right. \left \{ {{a=3,5-5b} \atop {10,5-15b-2b=2}} \right. \left \{ {{a=3,5-5b} \atop {10,5-17b=2}} \right.$

$\left \{ {{a=3,5-5b} \atop {-17b=2-10,5}} \right. \left \{ {{a=3,5-5b} \atop {b=-8,5:(-17)}} \right. \left \{ {{a=3,5-5* \frac{1}{2} } \atop {b= \frac{1}{2} }} \right. \left \{ {{a=3,5-2,5 } \atop {b= \frac{1}{2} }} \right. \left \{ {{a=1 } \atop {b= \frac{1}{2} }} \right. \left \{ {{ \frac{1}{x} =1} \atop { \frac{1}{y} = \frac{1}{2} }} \right. \left \{ {{x=1} \atop {y=2}} \right.$