a: \(\left\{{}\begin{matrix}\left(x-3\right)\left(2y+5\right)=\left(2x+7\right)\left(y-1\right)\\\left(4x+1\right)\left(3y-6\right)=\left(6x-1\right)\left(2y+3\right)\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}2xy+5x-6y-15=2xy-2x+7y-7\\12xy-24x+3y-6=12xy+18x-2y-3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}5x-6y-15=-2x+7y-7\\-24x+3y-6=18x-2y-3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}7x-13y=-7+15=8\\-42x+5y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}42x-78y=48\\-42x+5y=3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}-73y=51\\7x-13y=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{53}{71}\\7x=13y+8=13\cdot\dfrac{-53}{71}+8=-\dfrac{121}{71}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}y=-\dfrac{53}{71}\\x=-\dfrac{121}{497}\end{matrix}\right.\)

b: \(\left\{{}\begin{matrix}\left(x+y\right)\left(x-1\right)=\left(x-y\right)\left(x+1\right)+2xy\\\left(y-x\right)\left(y+1\right)=\left(y+x\right)\left(y-2\right)-2xy\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x^2-x+xy-y=x^2+x-xy-y+2xy\\y^2+y-xy-x=y^2-2y+xy-2x-2xy\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}-x-y=x-y\\y-x=-2y-2x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-2x=0\\3y=-x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=0\end{matrix}\right.\)

Ta có: \(\left\{{}\begin{matrix}x\left(x-3y\right)=4\left(y^2+2\right)\left(1\right)\\\left(xy-4\right)\left(x+y\right)=8\left(2\right)\end{matrix}\right.\)

\(\left(2\right)\Rightarrow xy-4;x+y\ne0\)

\(\left(1\right)\Leftrightarrow x^2-3xy-4y^2=8\) (*)

Từ (*) và (2) \(\Rightarrow x^2-3xy-4y^2=\left(xy-4\right)\left(x+y\right)\)

\(\Leftrightarrow x\left(x-4y\right)+y\left(x-4y\right)=\left(xy-4\right)\left(x+y\right)\)

\(\Leftrightarrow\left(x+y\right)\left(x-4y\right)=\left(x+y\right)\left(xy-4\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}x+y=0\left(L\right)\\x-4y=xy-4\end{matrix}\right.\) \(\Leftrightarrow x\left(1-y\right)+4\left(1-y\right)=0\)

\(\Leftrightarrow\left(x+4\right)\left(1-y\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-4\\y=1\end{matrix}\right.\)

x = -4 thay vào (*), ta được: \(16-3.\left(-4\right)y-4y^2=8\)

\(\Leftrightarrow8+12y-4y^2=0\) \(\Leftrightarrow y^2-3y-2=0\) 

\(\Leftrightarrow y=\dfrac{3\pm\sqrt{17}}{2}\) ( dùng \(\Delta\) )

y=1 thay vào (*), ta được: \(x^2-3x-4=8\)

\(\Leftrightarrow x^2-3x-12=0\) \(\Leftrightarrow x=\dfrac{3\pm\sqrt{57}}{2}\)

Vậy ...

a: Thay x=1 và y=-5 vào hệ, ta được:

\(\left\{{}\begin{matrix}3a\cdot1-\left(b+1\right)\cdot\left(-5\right)=93\\-5\cdot b+4\cdot a\cdot1=-3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}3a+5\left(b+1\right)=93\\4a-5b=-3\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}3a+5b=88\\4a-5b=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7a=85\\3a+5b=88\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}a=\dfrac{85}{7}\\5b=88-3a=88-3\cdot\dfrac{85}{7}=\dfrac{361}{7}\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}a=\dfrac{85}{7}\\b=\dfrac{361}{35}\end{matrix}\right.\)

b: Thay x=3 và y=-1 vào hệ, ta được:

\(\left\{{}\begin{matrix}\left(a-2\right)\cdot3+5b\cdot\left(-1\right)=25\\2a\cdot3-\left(-1\right)\left(b-2\right)=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3a-6-5b=25\\6a+b-2=5\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}3a-5b=31\\6a+b=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6a-10b=62\\6a+b=7\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}-11b=55\\6a+b=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}b=-5\\6a=7-b=7-\left(-5\right)=12\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}b=-5\\a=2\end{matrix}\right.\)

\(B=\left(\dfrac{x+2\sqrt{x}}{\sqrt{x}}+\sqrt{x}-2\right):\sqrt{x}\left(x>0\right)\\ =\left[\dfrac{\sqrt{x}\left(\sqrt{x}+2\right)}{\sqrt{x}}+\sqrt{x}-2\right].\dfrac{1}{\sqrt{x}}\\ =\left(\sqrt{x}+2+\sqrt{x}-2\right).\dfrac{1}{\sqrt{x}}\\ =\dfrac{2\sqrt{x}}{\sqrt{x}}=2\)

aaa

Số bé là:

  (56-14):2=21

Số lớn là: 

  21+14=35

Nếu bạn không dùng đến điểm O thì theo mình nghĩ sẽ không sao bạn nhé! Tuy nhiên để giải toán chắc chắn và chính xác chúng mình nên vẽ hình theo dữ kiện đề bài cho!