Question

Giải PT: 

\(a,\hept{\begin{cases}|x|+|y-3|=1\\y-|x|=3\end{cases}}\)

\(b,\hept{\begin{cases}x-4y=5\\2|x-2y|+|x+y|=7\end{cases}}\)\(c,\hept{\begin{cases}|x+1|+|y+1|=5\\|x+1|=4y-4\end{cases}}\)

Answer 1

Ta có:

\(\hept{\begin{cases}|x+1|+|y+1|=5\left(1\right)\\|x+1|=4y-4\left(2\right)\end{cases}}\)

Thay (2) vào (1):

\(4y-4+|y-1|=5\left(3\right)\)

+Nếu \(y\ge-1\Rightarrow4y-4+y+1=5\Rightarrow5y=8\Rightarrow y=\frac{8}{5}\left(TM\right)\)

Thay y = 8/5 vào (2) ta có: 

\(|x+1|=4.\frac{8}{5}-4\)

\(\Leftrightarrow|x+1|=\frac{12}{5}\)

\(\Leftrightarrow\orbr{\begin{cases}x+1=\frac{12}{5}\\x+1=\frac{-12}{5}\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{7}{5}\\x=-\frac{17}{5}\end{cases}}\)

+Nếu \(y\le-1\Rightarrow4y-4-y-1=5\Rightarrow3y=10\Rightarrow y=\frac{10}{3}\left(L\right)\)