# Variable intervals from system of inequalities ( <mtable rowspacing="4pt" columnspac

glycleWogry 2022-06-21 Answered
Variable intervals from system of inequalities
$\left(\begin{array}{cc}-1& 0\\ 1& 0\\ 0& -1\\ 1& -1\\ -2& 1\end{array}\right)\left(\begin{array}{c}i\\ j\end{array}\right)<\left(\begin{array}{c}20\\ 20\\ 10\\ 0\\ 20\end{array}\right)$
and I need to find possible intervals of i and j.
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## Answers (2)

Jake Mcpherson
Answered 2022-06-22 Author has 23 answers
The system is actually not too complicated. If you multiply them out you should get
-i < 20
i < 20
-j < 10
i-j < 0
-2i + j < 20
From the 2nd inequality, we have our desired upper bound for i. For the lower bound of -15, combine j > -10 and -2i + j < 20.
The 3rd inequality gives us our desired lower bound for j. As for the upper bound of 60, combine i < 20 and -2i+j < 20.
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excluderho
Answered 2022-06-23 Author has 8 answers
$\left(\begin{array}{cc}-1& 0\\ 1& 0\\ 0& -1\\ 1& -1\\ -2& 1\end{array}\right)\left(\begin{array}{c}i\\ j\end{array}\right)<\left(\begin{array}{c}20\\ 20\\ 10\\ 0\\ 20\end{array}\right)$
$\left(\begin{array}{c}-i\\ i\\ -j\\ i-j\\ -2i+j\end{array}\right)<\left(\begin{array}{c}20\\ 20\\ 10\\ 0\\ 20\end{array}\right)$
$\left(\begin{array}{c}-i<20\\ i<20\\ -j<10\\ i
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