24: \(\left\{{}\begin{matrix}2\left(x+y\right)-\left(x-y\right)=1\\\left(x+y\right)-3\left(x-y\right)=-5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+2y-x+y=1\\x+y-3x+3y=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+3y=1\\-2x+4y=-5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+6y=2\\-2x+4y=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+6y-2x+4y=2-5\\-x+2y=-\dfrac{5}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}10y=-3\\x-2y=\dfrac{5}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{3}{10}\\x=2y+\dfrac{5}{2}=-\dfrac{3}{5}+\dfrac{5}{2}=\dfrac{19}{10}\end{matrix}\right.\)
25: \(\left\{{}\begin{matrix}2x+1=x+2y\\x-y=2x+y+1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-x-2y=-1\\x-y-2x-y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x-2y=-1\\-x-2y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x-2y-x-2y=-1+1\\x-2y=-1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-4y=0\\x=2y-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=0\\x=-1\end{matrix}\right.\)
26: \(\left\{{}\begin{matrix}2\left(x-2y\right)+3\left(x+2y\right)=4\\\left(x-y\right)+2\left(x+y\right)=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x-4y+3x+6y=4\\x-y+2x+2y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x+2y=4\\3x+y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}5x+2y=4\\6x+2y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-x=2\\3x+y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=1-3x=1-3\cdot\left(-2\right)=7\end{matrix}\right.\)
27: \(\left\{{}\begin{matrix}\left(x+4\right)\left(y+4\right)=xy+216\\\left(x+2\right)\left(y-5\right)=xy-50\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}xy+4x+4y+16=xy+216\\xy-5x+2y-10=xy-50\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x+4y=200\\-5x+2y=-40\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+2y=100\\-5x+2y=-40\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}7x=140\\x+y=50\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=20\\y=50-x=50-20=30\end{matrix}\right.\)
`24)`
\(\left\{{}\begin{matrix}2\left(x+y\right)-\left(x-y\right)=1\\\left(x+y\right)-3\left(x-y\right)=-5\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}2x+2y-x+y=1\\x+y-3x+3y=-5\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}x+3y=1\\-2x+4y=-5\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}x=1-3y\\-2\left(1-3y\right)+4y=-5\end{matrix}\right.\) `<=>` \(\left\{{}\begin{matrix}x=1-3y\\-2+6y+4y=-5\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}x=1-3y\\10y=-3\end{matrix}\right.\) `<=>` \(\left\{{}\begin{matrix}x=1-3.\left(-\dfrac{3}{10}\right)\\y=-\dfrac{3}{10}\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}x=\dfrac{19}{10}\\y=-\dfrac{3}{10}\end{matrix}\right.\)
Vậy hpt có nghiệm `(x;y)=((19)/(10) ; (-3)/(10))`
`25)`
\(\left\{{}\begin{matrix}2x+1=x+2y\\x-y=2x+y+1\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}2x-x-2y=-1\\x-y-2x-y=1\end{matrix}\right.\) `<=>` \(\left\{{}\begin{matrix}x-2y=-1\\-x-2y=1\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}2x=-2\\-x-2y=1\end{matrix}\right.\) `<=>` \(\left\{{}\begin{matrix}x=-1\\-\left(-1\right)-2y=1\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}x=-1\\y=0\end{matrix}\right.\)
Vậy hpt có nghiệm `(x;y)=(-1;0)`
`26)`
\(\left\{{}\begin{matrix}2\left(x-2y\right)+3\left(x+2y\right)=4\\\left(x-y\right)+2\left(x+y\right)=1\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}2x-4y+3x+6y=4\\x-y+2x+2y=1\end{matrix}\right.\) `<=>` \(\left\{{}\begin{matrix}5x+2y=4\\3x+y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5x+2y=4\\6x+2y=2\end{matrix}\right.\) `<=>` \(\left\{{}\begin{matrix}-x=2\\6x+2y=2\end{matrix}\right.\)
`<=> {(x=-2),(6.(-2) + 2y=2):}`
`<=>{(x=-2),(y=7):}`
Vậy hpt có nghiệm `(x;y)=(-2;7)`
`27)`
\(\left\{{}\begin{matrix}\left(x+4\right)\left(y+4\right)=xy+216\\\left(x+2\right)\left(y-5\right)=xy-50\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}xy+4x+4y+16=xy+216\\xy-5x+2y-10=xy-50\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}xy+4x+4y-xy=216-16\\xy-5x+2y-xy=-50+10\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}4x+4y=200\\-5x+2y=-40\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}x+y=50\\-5x+2y=-40\end{matrix}\right.\) `<=>` \(\left\{{}\begin{matrix}x=50-y\\-5\left(50-y\right)+2y=-40\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}x=50-y\\-250+5y+2y=-40\end{matrix}\right.\)
`<=>` \(\left\{{}\begin{matrix}x=50-y\\7y=210\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=50-30\\y=30\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=20\\y=30\end{matrix}\right.\)
Vậy hpt có nghiệm `(x;y)=(20;30)`
