HPT quy về hpt bậc nhất hai ẩn
1)2x − 11y = −7
10x + 11y = 31
2) 3x − 2y = 11
4x − 5y = 3
3) 3(x + 1) − 2(y − 1) = 4
4(x − 2) + 3(y + 1) = 5
4) x + 4y = 6
4x + 16y = 5
5) x(y + 2) − y(x + 1) = 3
2x(y + 1) − y(2x + 3) = 1
6) 3(x + 1) + 2(x + 2y) = 4
4(x + 1) − (x + 2y) = 9
7) 5(x + 2y) − 3(x − y) = 99
x − 3y = 7x − 4y − 17
8 ) x(2y − 1) − y(2x + 1) = −4
x(3y + 1) + y(−3x + 2) = 5
9) (3x + 2)(2y − 3) = 6xy
(4x + 5)(y − 5) = 4xy
1: \(\left\{{}\begin{matrix}2x-11y=-7\\10x+11y=31\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-11y+10x+11y=-7+31\\2x-11y=-7\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}12x=24\\11y=2x+7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\11y=2\cdot2+7=11\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)
2: \(\left\{{}\begin{matrix}3x-2y=11\\4x-5y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}12x-8y=44\\12x-15y=9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}12x-8y-12x+15y=44-9\\3x-2y=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7y=35\\3x=2y+11\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=5\\x=\dfrac{2y+11}{3}=\dfrac{2\cdot5+11}{3}=\dfrac{21}{3}=7\end{matrix}\right.\)
3: \(\left\{{}\begin{matrix}3\left(x+1\right)-2\left(y-1\right)=4\\4\left(x-2\right)+3\left(y+1\right)=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x+3-2y+2=4\\4x-8+3y+3=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x-2y=-1\\4x+3y=5+8-3=10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}12x-8y=-4\\12x+9y=30\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}12x-8y-12x-9y=-4-30\\3x-2y=-1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-17y=-34\\3x=2y-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2\\x=\dfrac{2y-1}{3}=\dfrac{2\cdot2-1}{3}=1\end{matrix}\right.\)
4: \(\left\{{}\begin{matrix}x+4y=6\\4x+16y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4x+16y=24\\4x+16y=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x+16y-4x-16y=24-5\\x+4y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}0x=19\\4y=6-x\end{matrix}\right.\)(vô lý)
vậy: Hệ vô nghiệm
5: \(\left\{{}\begin{matrix}x\left(y+2\right)-y\left(x+1\right)=3\\2x\left(y+1\right)-y\left(2x+3\right)=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}xy+2x-xy-y=3\\2xy+2x-2xy-3y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-y=3\\2x-3y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x-y-2x+3y=3-1\\2x-y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2y=2\\2x=y+3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=1\\x=\dfrac{y+3}{2}=\dfrac{1+3}{2}=2\end{matrix}\right.\)
6: \(\left\{{}\begin{matrix}3\left(x+1\right)+2\left(x+2y\right)=4\\4\left(x+1\right)-\left(x+2y\right)=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+3+2x+4y=4\\4x+4-x-2y=9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}5x+4y=1\\3x-2y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x+4y=1\\6x-4y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x+4y+6x-4y=1+10\\3x-2y=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}11x=11\\2y=3x-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=\dfrac{3x-5}{2}=\dfrac{3\cdot1-5}{2}=\dfrac{3-5}{2}=-1\end{matrix}\right.\)
7: \(\left\{{}\begin{matrix}5\left(x+2y\right)-3\left(x-y\right)=99\\x-3y=7x-4y-17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}5x+10y-3x+3y=99\\x-3y-7x+4y=-17\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x+13y=99\\-6x+y=-17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}6x+39y=297\\-6x+y=-17\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x+39y-6x+y=297-17\\6x-y=17\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}40y=280\\6x=y+17\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=7\\x=\dfrac{y+17}{6}=\dfrac{7+17}{6}=\dfrac{24}{6}=4\end{matrix}\right.\)
8:
\(\left\{{}\begin{matrix}x\left(2y-1\right)-y\left(2x+1\right)=-4\\x\left(3y+1\right)+y\left(-3x+2\right)=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2xy-x-2xy-y=-4\\3xy+x-3xy+2y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-x-y=-4\\x+2y=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-x-y+x+2y=-4+5\\x+y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=4-y=4-1=3\end{matrix}\right.\)
9:
\(\left\{{}\begin{matrix}\left(3x+2\right)\left(2y-3\right)=6xy\\\left(4x+5\right)\left(y-5\right)=4xy\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}6xy-9x+4y-6=6xy\\4xy-20x+5y-25=4xy\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-9x+4y=6\\-20x+5y=25\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-180x+80y=120\\-180x+45y=225\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-180x+80y+180x-45y=120-225\\9x-4y=-6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}35y=-105\\9x=4y-6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-3\\x=\dfrac{4y-6}{9}=\dfrac{4\cdot\left(-3\right)-6}{9}=\dfrac{-18}{9}=-2\end{matrix}\right.\)
\(1.\left\{{}\begin{matrix}2x-11y=-7\\10x+11y=31\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-11y=-7\\12x=24\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}2\cdot2-11y=-7\\x=24:12=2\end{matrix}\right. \Leftrightarrow\left\{{}\begin{matrix}11y=4+7=11\\x=2\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=11:11=1\\x=2\end{matrix}\right.\\ 2.\left\{{}\begin{matrix}3x-2y=11\\4x-5y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}12x-8y=44\\12x-15y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x-2y=11\\7y=35\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}3x-2\cdot5=11\\y=35:7=5\end{matrix}\right. \Leftrightarrow\left\{{}\begin{matrix}3x=11+10=21\\y=5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=21:3=7\\y=5\end{matrix}\right.\\ 3.\left\{{}\begin{matrix}3\left(x+1\right)-2\left(y-1\right)=4\\4\left(x-2\right)+3\left(y+1\right)=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+3-2y+2=4\\4x-8+3y+3=5\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}3x-2y=4-5=-1\\4x+3y=5+5=10\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}9x-6y=-3\\8x+6y=20\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x-2y=-1\\17x=17\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}3-2y=-1\\x=17:17=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2y=3+1=4\\x=1\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{4}{2}=2\\x=1\end{matrix}\right.\)
