Question

\(\left|x+5\right|+\left|y-2\right|\le4\\ 5\left|x+1\right|+\left|y-2\right|\le7\)

Tìm các cặp số nguyên ( x ; y ) thỏa mãn.

Answer 1

a)

\(\left\{{}\begin{matrix}\left|x+5\right|\le4\\x\in Z\end{matrix}\right.\) \(\Leftrightarrow-4\le x+5\le4\Rightarrow-9\le x\le-1\)

\(-4+\left|x+5\right|\le y-2\le4-\left|x+5\right|\)

\(-2+\left|x+5\right|\le y\le6-\left|x+5\right|\)

x={-1;-9}=> \(2\le y\le6-4\Rightarrow y=2\)

x={-2;-8}=> \(1\le y\le3\Rightarrow y=1;2;3\)

x={-3;-7} => \(0\le y\le4\Rightarrow y=0;1;2;3;4\)

x={-4;-6}=>\(-1\le y\le5\Rightarrow y=\left\{-1;0;1;2;3;4;5\right\}\)

x={-5}=> \(-2\le y\le6\Rightarrow y=\left\{-2;-1;0;1;2;3;4;5;6\right\}\)

(x;y)=(-1;2); (-2;y={1;2;3}) ....

b) tương tự