a/ |2x - 3| + |y - 2| = 0

Vì: \(\left\{{}\begin{matrix}\left|2x-3\right|\ge0\forall x\\\left|y-2\right|\ge0\forall y\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}2x-3=0\\y-2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=2\end{matrix}\right.\)

b/ |3x - 4| + |x - y| = 0

Vì: \(\left\{{}\begin{matrix}\left|3x-4\right|\ge0\forall x\\\left|x-y\right|\ge0\forall x;y\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}3x-4=0\\x-y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{4}{3}\\x=y=\dfrac{4}{3}\end{matrix}\right.\)

Vậy x = y = 4/3

c/ \(\left|2x+y-1\right|+\left|2y-3\right|=0\)

Vì: \(\left\{{}\begin{matrix}\left|2x+y-1\right|\ge0\forall x;y\\\left|2y-3\right|\ge0\forall y\end{matrix}\right.\)

=> \(\left\{{}\begin{matrix}2x+y-1=0\\2y-3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-1=-y\\y=\dfrac{3}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}2x-1=-\dfrac{3}{2}\\y=\dfrac{3}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{4}\\y=\dfrac{3}{2}\end{matrix}\right.\)

Vậy--..

d/ \(\left|x+y-5\right|+\left|2x-y+8\right|=0\)

Vì: \(\left\{{}\begin{matrix}\left|x+y-5\right|\ge0\\\left|2x-y+8\right|\ge0\end{matrix}\right.\)∀x;y

=> \(\left\{{}\begin{matrix}x+y-5=0\\2x-y+8=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x+y=5\\2x-y=-8\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=5-y\\2\left(5-y\right)-y=-8\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=5-y\\10-2y-y=-8\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=5-y\\-3y=-18\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=5-y\\y=6\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=5-6=-1\\y=6\end{matrix}\right.\)

Vậy x = -1; y = 6