Giải các hệ phương trình:
$a)  \begin{cases}(x-4)(y-3)=20 \\ 4x-3y=15\end{cases}               b) \begin{cases}\frac{1+x+x^2}{1+y+y^2} =3 \\ x+y=6\end{cases}            c) \begin{cases}\frac{3}{x+5}+\frac{2}{y-3}=2 \\ \frac{4}{x-2}+\frac{1}{6-y} =0 \end{cases}   $.
$d) \begin{cases}\frac{\sqrt{x} }{\sqrt{y} }+\frac{\sqrt{y} }{\sqrt{x} }=\frac{5}{2}  \\ x+y=25 \end{cases}                             e) \begin{cases}2x^2-5xy+y^2+10x+12y=100 \\2x-3 y=1 \end{cases} $
a) Đáp số:  $S=\left\{ {(1; \frac{-11}{3} ),  (9; 7)} \right\}$
b) Thế $x=6-y$ vào phương trình thứ nhất, ta thu dược kết quả $S=\left\{ {(4; 2) , (16; -10)} \right\}$
c) Điều kiện:      $x\neq- 5;   x\neq2;  y\neq 3;    y\neq 6$
  Hướng dẫn : Từ PT thứ hai $4(6-y)+(x-2)=0 \Leftrightarrow  x=4y-22$ và thay điều này vào PT thứ nhất.
Đáp số:    $S=\left\{ {(-2; 5), (\frac{-15}{2};  \frac{29}{8} )} \right\}$
d) Điều kiện:     $x> 0;  y>0$.       Đáp số:       S = {$(5; 20), (20; 5)$}
e) Đáp số:      $S=\left\{ {(11; 7), (\frac{85}{8};\frac{27}{4})} \right\}$

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