Giải các hệ phương trình sau:
a) \(\left\{{}\begin{matrix}2x+5y=5\\3x-5y=-30\end{matrix}\right.\) b) \(\left\{{}\begin{matrix}4x-3y=-5\\3x+2y=-8\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}3x+3y=9\\4x-2y=-2\end{matrix}\right.\) d) \(\left\{{}\begin{matrix}5x-4y=32\\6x+2y=18\end{matrix}\right.\)
e) \(\left\{{}\begin{matrix}2x-3y+5=0\\3x+5y-21=0\end{matrix}\right.\) f) \(\left\{{}\begin{matrix}x-y\sqrt{2}=0\\2x\sqrt{2}+y=5\end{matrix}\right.\)
g) \(\left\{{}\begin{matrix}5x+4y=-3\\3x+2y=11\end{matrix}\right.\) h) \(\left\{{}\begin{matrix}2x-4y=12\\5x+3y=17\end{matrix}\right.\)
e.
\(\left\{{}\begin{matrix}2x-3y+5=0\\3x+5y-21=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}10x-15y=-25\\9x+15y=63\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}19x=38\\3x+5y=21\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=\dfrac{21-3x}{5}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=3\end{matrix}\right.\)
f.
\(\left\{{}\begin{matrix}x-y\sqrt{2}=0\\2x\sqrt{2}+y=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-y\sqrt{2}=0\\4x+y\sqrt{2}=5\sqrt{2}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5x=5\sqrt{2}\\2x\sqrt{2}+y=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\sqrt{2}\\y=5-2x\sqrt{2}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\sqrt{2}\\y=1\end{matrix}\right.\)
a.
\(\Leftrightarrow\left\{{}\begin{matrix}5x=-25\\3x-5y=-30\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-5\\y=\dfrac{3x+30}{5}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-5\\y=3\end{matrix}\right.\)
b.
\(\Leftrightarrow\left\{{}\begin{matrix}8x-6y=-10\\9x+6y=-24\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}17x=-34\\9x+6y=-24\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=\dfrac{-24-9x}{6}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=-2\\y=-1\end{matrix}\right.\)
c.
\(\left\{{}\begin{matrix}3x+3y=9\\4x-2y=-2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y=3\\2x-y=-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x=2\\2x-y=-1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2}{3}\\y=2x+1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2}{3}\\y=\dfrac{7}{3}\end{matrix}\right.\)
d.
\(\left\{{}\begin{matrix}5x-4y=32\\6x+2y=18\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5x-4y=32\\12x+4y=36\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5x-4y=32\\17x=68\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=\dfrac{3x-32}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=-3\end{matrix}\right.\)
g.
\(\left\{{}\begin{matrix}5x+4y=-3\\3x+2y=11\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5x+4y=-3\\-6x-4y=-22\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-x=-25\\3x+2y=11\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=25\\y=\dfrac{11-3x}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=25\\y=-32\end{matrix}\right.\)
h.
\(\left\{{}\begin{matrix}2x-4y=12\\5x+3y=17\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}6x-12y=36\\20x+12y=68\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}26x=104\\5x+3y=17\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=\dfrac{17-5x}{3}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=-1\end{matrix}\right.\)