Bài 1:
\(a.\left\{{}\begin{matrix}4x+y=9\\8x+3y=19\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}8x+2y=18\\8x+3y=19\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\4x+1=9\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=1\\4x=9-1=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=1\\x=\dfrac{8}{4}=2\end{matrix}\right.\\ b.\left\{{}\begin{matrix}3x-2y=11\\4x-5y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}12x-8y=44\\12x-15y=9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7y=35\\3x-2y=11\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{35}{7}=5\\3x-10=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=5\\3x=11+10=21\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=5\\x=\dfrac{21}{3}=7\end{matrix}\right.\\ c.\left\{{}\begin{matrix}5x-4y=3\\2x+y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5x-4y=3\\8x+4y=16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13x=19\\2x+y=4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{19}{13}\\\dfrac{38}{13}+y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{19}{13}\\y=4-\dfrac{38}{13}=\dfrac{14}{13}\end{matrix}\right.\)
Bài 2:
a: \(\left\{{}\begin{matrix}4x+3y=13\\5x-3y=-31\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4x+3y+5x-3y=13-31\\4x+3y=13\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}9x=-18\\3y=13-4x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=\dfrac{13-4x}{3}=\dfrac{13-4\cdot\left(-2\right)}{3}=\dfrac{13+8}{3}=7\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}7x+5y=19\\3x+5y=31\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}7x+5y-3x-5y=19-31\\3x+5y=31\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x=-12\\5y=31-3x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\\5y=31-3\cdot\left(-3\right)=40\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-3\\y=8\end{matrix}\right.\)
c: \(\left\{{}\begin{matrix}7x-5y=3\\3x+10y=62\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}14x-10y=6\\3x+10y=62\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}14x-10y+3x+10y=6+62\\7x-5y=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}17x=68\\5y=7x-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=\dfrac{7x-3}{5}=\dfrac{7\cdot4-3}{5}=\dfrac{25}{5}=5\end{matrix}\right.\)
d: \(\left\{{}\begin{matrix}x+5y=-5\\3x+2y=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+15y=-15\\3x+2y=11\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x+15y-3x-2y=-15-11\\x+5y=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13y=-26\\x=-5-5y\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=-2\\x=-5-5\cdot\left(-2\right)=-5+10=5\end{matrix}\right.\)
e: \(\left\{{}\begin{matrix}3x+2y=8\\4x-3y=-12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x+6y=24\\8x-6y=-24\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}9x+6y+8x-6y=24-24=0\\3x+2y=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\2y=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=0\\y=4\end{matrix}\right.\)
f: \(\left\{{}\begin{matrix}2x+3y=-2\\3x-2y=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4x+6y=-4\\9x-6y=-9\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x+6y+9x-6y=-4-9\\2x+3y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}13x=-13\\3y=-2-2x\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-1\\y=\dfrac{-2x-2}{3}=\dfrac{-2\cdot\left(-1\right)-2}{3}=\dfrac{2-2}{3}=0\end{matrix}\right.\)
Bài 3:
a: \(\left\{{}\begin{matrix}-x+2y=-4\left(x-1\right)\\5x+3y=-\left(x+y\right)+8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-x+2y+4x-4=0\\5x+3y+x+y=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+2y=4\\6x+4y=8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x+2y=4\\3x+2y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3x+2y-3x-2y=4-4\\3x+2y=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}0x=0\\2y=4-3x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\in R\\y=\dfrac{4-3x}{2}\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}9x-6y=4\\3\left(4x-3y\right)=-3x+y+7\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}9x-6y=4\\12x-9y+3x-y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x-6y=4\\15x-10y=7\end{matrix}\right.\)
Vì \(\dfrac{9}{15}=\dfrac{-6}{-10}\ne\dfrac{4}{7}\)
nên hệ phương trình vô nghiệm
c: \(\left\{{}\begin{matrix}3\left(x+1\right)+2y=-x\\5\left(x+y\right)=-3x+y-5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x+3+2y+x=0\\5x+5y+3x-y=-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4x+2y=-3\\8x+4y=-5\end{matrix}\right.\)
Vì \(\dfrac{4}{8}=\dfrac{2}{4}\ne\dfrac{-3}{-5}\)
nên hệ phương trình vô nghiệm
d: \(\left\{{}\begin{matrix}2\left(2x+3y\right)=3\left(2x-3y\right)+10\\4x-3y=4\left(6y-2x\right)+3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x+6y-6x+9y=10\\4x-3y-24x+8y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-2x+15y=10\\-20x+5y=3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-20x+150y=100\\-20x+5y=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}145y=97\\-2x+15y=10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=\dfrac{97}{145}\\15y=2x+10=2\cdot\dfrac{97}{145}+10=\dfrac{1644}{145}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=\dfrac{97}{145}\\y=\dfrac{548}{725}\end{matrix}\right.\)
