Bài 2:
1: \(\left\{{}\begin{matrix}4x+y=2\\8x+3y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=2-4x\\8x+3\left(2-4x\right)=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=2-4x\\8x+6-12x=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-4x=-1\\y=2-4x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{4}\\y=2-4\cdot\dfrac{1}{4}=2-1=1\end{matrix}\right.\)
2: \(\left\{{}\begin{matrix}x-y=m\\2x+y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=x-m\\2x+x-m=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x=m+4\\y=x-m\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{m+4}{3}\\x=\dfrac{m+4}{3}-m=\dfrac{m+4-3m}{3}=\dfrac{-2m+4}{3}\end{matrix}\right.\)
3: \(\left\{{}\begin{matrix}3x+2y=6\\x-y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=y+2\\3\left(y+2\right)+2y=6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=y+2\\5y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=0\\x=0+2=2\end{matrix}\right.\)
4: \(\left\{{}\begin{matrix}2x-3y=1\\-4x+6y=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=3y+1\\-2\left(3y+1\right)+6y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=3y+1\\-6y-2+6y=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{3y+1}{2}\\-2=2\left(vôlý\right)\end{matrix}\right.\)
vậy: hệ vô nghiệm
5: \(\left\{{}\begin{matrix}2x+3y=5\\5x-4y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=5-3y\\2,5\cdot2x-4y=1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{5-3y}{2}\\2,5\left(5-3y\right)-4y=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}12,5-7,5y-4y=1\\x=\dfrac{5-3y}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}11,5y=12,5-1=11,5\\x=\dfrac{5-3y}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=\dfrac{5-3}{2}=1\end{matrix}\right.\)
6: \(\left\{{}\begin{matrix}3x-y=7\\x+2y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=3x-7\\x+2\left(3x-7\right)=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=3x-7\\7x-14=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=3\cdot2-7=6-7=-1\end{matrix}\right.\)
7: \(\left\{{}\begin{matrix}x+4y=2\\3x+2y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-4y+2\\3\left(-4y+2\right)+2y=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-4y+2\\-12y+6+2y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-4y+2\\-10y=-2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-4y+2\\y=\dfrac{1}{5}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-4\cdot\dfrac{1}{5}+2=2-\dfrac{4}{5}=\dfrac{6}{5}\\y=\dfrac{1}{5}\end{matrix}\right.\)
8: \(\left\{{}\begin{matrix}-x-y=2\\-2x-3y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+y=-2\\2x+3y=-9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-2-y\\2\left(-y-2\right)+3y=-9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-y-2\\-2y-4+3y=-9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y-4=-9\\x=-y-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-5\\x=5-2=3\end{matrix}\right.\)
9: \(\left\{{}\begin{matrix}2x-3y=2\\-4x+6y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=3y+2\\-2\cdot2x+6y=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x=3y+2\\-2\left(3y+2\right)+6y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-6y-4+6y=2\\x=\dfrac{3y+2}{2}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-4=2\left(sai\right)\\x=\dfrac{3y+2}{2}\end{matrix}\right.\)
Vậy: Hệ vô nghiệm
Bài 3:
\(\left\{{}\begin{matrix}\left|x-1\right|+\left|y-2\right|=1\\\left|x-1\right|+3y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\left|x-1\right|+\left|y-2\right|-\left|x-1\right|-3y=1-3\\\left|x-1\right|+3y=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\left|y-2\right|-3y=-2\\\left|x-1\right|+3y=3\end{matrix}\right.\)
|y-2|-3y=-2(1)
TH1: y>=2
(1) sẽ trở thành: \(y-2-3y=-2\)
=>-2y=0
=>y=0(loại)
TH2: y<2
(1) sẽ trở thành 2-y-3y=-2
=>2-4y=-2
=>4y=4
=>y=1(nhận)
|x-1|+3y=3
=>|x-1|+3=3
=>|x-1|=0
=>x-1=0
=>x=1
