Реши систему уравнений 4/x+y-1 - 5/2x-y+3 + 5/2=0 3/x+y-1 + 1/2x-y+3 + 7/5=0

1. Обозначим:

p = 1 / (x + y - 1); q = 1 / (2x - y + 3).

{4 / (x + y - 1) - 5 / (2x - y + 3) + 5/2 = 0;

{3 / (x + y - 1) + 1 / (2x - y + 3) + 7/5 = 0;

{4p - 5q + 5/2 = 0;

{3p + q + 7/5 = 0;

{8p - 10q + 5 = 0;

{30p + 10q + 14 = 0;

{38p + 19 = 0;

{q = - 7/5 - 3p;

{38p = - 19;

{q = - 7/5 - 3p;

{p = - 1/2;

{q = - 1,4 - 3 * (-1/2);

{p = - 0,5;

{q = - 1,4 + 1,5;

{p = - 0,5;

{q = 0,1.

3. Найдем значения x и y:

{p = 1 / (x + y - 1);

{q = 1 / (2x - y + 3);

{x + y - 1 = 1 / p;

{2x - y + 3 = 1 / q;

{x + y - 1 = - 2;

{2x - y + 3 = 10;

{y = - x - 1;

{3x + 2 = 8;

{y = - x - 1;

{3x = 6;

{y = - 2 - 1;

{x = 2;

{y = - 3;

{x = 2.

Ответ: (2; - 3).