a: \(\left\{{}\begin{matrix}2x+3y=-2\\3x-2y=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=-3y-2\\3x-2y=-3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-1,5y-1\\3\left(-1,5y-1\right)-2y=-3\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-1,5y-1\\-4,5y-3-2y=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-1,5y-1\\-6,5y=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=0\\x=-1,5-1=-2,5\end{matrix}\right.\)
b: \(\left\{{}\begin{matrix}4x+3y=6\\2x+y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}4x+3y=6\\y=-2x\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x+3\cdot\left(-2x\right)=6\\y=-2x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-2x=6\\y=-2x=6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-3\\y=6\end{matrix}\right.\)
c: \(\left\{{}\begin{matrix}9x+8y=6\\2x-y=2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}9x+8y=6\\y=2x-2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}9x+8\left(2x-2\right)=6\\y=2x-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}25x-16=6\\y=2x-2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}25x=22\\y=2x-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{22}{25}\\y=2\cdot\dfrac{22}{25}-2=\dfrac{44}{25}-2=-\dfrac{6}{25}\end{matrix}\right.\)
d: \(\left\{{}\begin{matrix}x-6y=17\\5x+y=23\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=6y+17\\5\left(6y+17\right)+y=23\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=6y+17\\31y+85=23\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=6y+17\\31y=23-85=-62\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=6y+17\\y=-2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=6\cdot\left(-2\right)+17=5\\y=-2\end{matrix}\right.\)
e: \(\left\{{}\begin{matrix}7x+4y=74\\3x+2y=32\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2y=32-3x\\7x+4y=74\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2y=32-3x\\7x+2\left(32-3x\right)=74\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2y=32-3x\\7x+64-6x=74\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2y=32-3\cdot10=2\\x=10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=1\\x=10\end{matrix}\right.\)
f:
\(\left\{{}\begin{matrix}x-3y=6\\-2x+6y=-12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=3y+6\\-2\left(3y+6\right)+6y=-12\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=3y+6\\-6y-12+6y=-12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}0y=0\\x=3y+6\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y\in R\\x=3y+6\end{matrix}\right.\)
g: \(\left\{{}\begin{matrix}\dfrac{x}{3}+\dfrac{y}{4}-2=0\\5x-y=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{4x+3y}{12}=2\\5x-y=11\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}4x+3y=24\\5x-y=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=5x-11\\4x+3\left(5x-11\right)=24\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=5x-11\\4x+15x-33=24\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=5x-11\\19x=57\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=3\\y=5\cdot3-11=4\end{matrix}\right.\)
h: \(\left\{{}\begin{matrix}\dfrac{a}{5}+\dfrac{b}{3}=-\dfrac{1}{3}\\4a-5b-10=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3a+5b}{15}=\dfrac{-5}{15}\\4a-5b=10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3a+5b=-5\\4a-5b=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3a+5b+4a-5b=-5+10\\4a-5b=10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}7a=5\\5b=4a-10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=\dfrac{5}{7}\\b=\dfrac{4a-10}{5}=\dfrac{4\cdot\dfrac{5}{7}-10}{5}=\dfrac{4}{7}-2=-\dfrac{10}{7}\end{matrix}\right.\)
i: \(\left\{{}\begin{matrix}\dfrac{x}{2}=\dfrac{y}{3}\\x+y-10=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2}{3}y\\\dfrac{2}{3}y+y=10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{2}{3}y\\\dfrac{5}{3}y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=10:\dfrac{5}{3}=6\\x=\dfrac{2}{3}\cdot6=4\end{matrix}\right.\)
