21:
a: \(\Leftrightarrow\left\{{}\begin{matrix}3x+6y=15\\3x-5y=-18\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}11y=33\\x+2y=5\end{matrix}\right.\Leftrightarrow\left(x,y\right)=\left(-1;3\right)\)
b: \(\Leftrightarrow\left\{{}\begin{matrix}4x+2y=10\\3x+2y=27\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-17\\y=5-2x=5-2\cdot\left(-17\right)=39\end{matrix}\right.\)
c: \(\Leftrightarrow\left\{{}\begin{matrix}-8x+4y=-12\\3x+4y=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-11x=-22\\-2x+y=-3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=-3+2x=-3+2\cdot2=1\end{matrix}\right.\)
a.\(\left\{{}\begin{matrix}x-2y=5\left(1\right)\\3x-5y=-18\left(2\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=5-2y\left(1\right)\\3x-5y=-18\left(2\right)\end{matrix}\right.\)
Thế (1) vào (2):
\(\Rightarrow\left\{{}\begin{matrix}x=5-2y\left(1\right)\\3\cdot\left(5-2y\right)-5y=-18\left(2\right)\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=5-2y\left(1\right)\\15-6y-5y=-18\left(2\right)\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=5-2y\left(1\right)\\-11y=-18-15\left(2\right)\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=5-2y\left(1\right)\\-11y=-33\left(2\right)\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=5-2y\left(1\right)\\y=3\end{matrix}\right.\\\Leftrightarrow \left\{{}\begin{matrix}x=5-2\cdot3\\y=3\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}x=-1\\y=3\end{matrix}\right.\)
b. \(\left\{{}\begin{matrix}2x+y=5\left(1\right)\\3x+2y=27\left(2\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=5-2x\left(1\right)\\3x+2y=27\left(2\right)\end{matrix}\right.\)
Thế (1) vào (2):
\(\Rightarrow\left\{{}\begin{matrix}y=5-2x\left(1\right)\\3x+2\left(5-2x\right)=27\left(2\right)\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=5-2x\\3x+10-4x=27\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=5-2x\\3x-4x=27-10\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=5-2x\\-x=17\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=5-2x\\x=-17\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=5-2\cdot\left(-17\right)\\x=-17\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=39\\x=-17\end{matrix}\right.\)
c. \(\left\{{}\begin{matrix}-2x+y=-3\left(1\right)\\3x+4y=10\left(2\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=-3+2x\left(1\right)\\3x+4y=10\left(2\right)\end{matrix}\right.\)
Thế (1) vào (2):
\(\Rightarrow\left\{{}\begin{matrix}y=-3+2x\left(1\right)\\3x+4\left(-3+2x\right)=10\left(2\right)\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=-3+2x\\3x+\left(-12\right)+8x=10\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=-3+2x\\3x+8x=10+12\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=-3+2x\\11x=22\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=-3+2x\\x=2\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}y=-3+2\cdot2\\x=2\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}y=1\\x=2\end{matrix}\right.\)
d. \(\left\{{}\begin{matrix}\sqrt{2}x-3y=-2\sqrt{2}\\2x+\sqrt{2}y=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{2}x=-2\sqrt{2}+3y\\2x+\sqrt{2}y=4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-2\sqrt{2}+3y}{\sqrt{2}}\left(1\right)\\2x+\sqrt{2}y=4\left(2\right)\end{matrix}\right.\)
Thế (1) vào (2):
\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{-2\sqrt{2}+3y}{\sqrt{2}}\left(1\right)\\2\cdot\left(\dfrac{-2\sqrt{2}+3y}{\sqrt{2}}\right)+\sqrt{2}y=4\left(2\right)\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-2\sqrt{2}+3y}{\sqrt{2}}\\\dfrac{-4\sqrt{2}}{\sqrt{2}}+\dfrac{6y}{\sqrt{2}}+\sqrt{2}y=4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-2\sqrt{2}+3y}{\sqrt{2}}\\-4+\dfrac{6y}{\sqrt{2}}+\sqrt{2}y=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-2\sqrt{2}+3y}{\sqrt{2}}\\\dfrac{6y}{\sqrt{2}}+\dfrac{\sqrt{2}y\cdot\sqrt{2}}{\sqrt{2}}=4+4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-2\sqrt{2}+3y}{\sqrt{2}}\\\dfrac{6y+2y}{\sqrt{2}}=8\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-2\sqrt{2}+3y}{\sqrt{2}}\\\dfrac{8y}{\sqrt{2}}=8\end{matrix}\right.\\\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-2\sqrt{2}+3y}{\sqrt{2}}\\y=\dfrac{8}{\dfrac{8}{\sqrt{2}}}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-2\sqrt{2}+3y}{\sqrt{2}}\\y=\sqrt{2}\end{matrix}\right. \)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-2\sqrt{2}+3\cdot\sqrt{2}}{\sqrt{2}}\\y=\sqrt{2}\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=1\\y=\sqrt{2}\end{matrix}\right.\)
