Fill in the blank/s: A system of linear inequalities is used to represent restrictions, or ________ on a function that must be maximised or minim,ised. Use the graph of such a system of inequalities, the maximum and minimum values of the function occur at one or more of the _____________ points.

Graph the function rule. Explain why the graph is continuous or discrete. Graph $y=-|x|+2y=-\mid x\mid +2$

These four inequalities define a hollow (zero volume) cube. Is it possible to describe a hollow cube using a smaller system of (real scalar generalized-polynomial) inequalities?
$\begin{array}{rcl}{x}^2& \le & 1\\ y^2& \le & 1\\ z^2& \le & 1\\ (x^2-1{)}^2(y^2-1{)}^2(z^2-1{)}^2& \le & 0\end{array}$

Determine whether the orderred pair is a solution to the system of inequlities
x+y<4
${\displaystyle y\le 2x+1}$
a. (0,1)
b. (3,1)
c. (2,0)
d. (1,4)

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.

Given the system
${\mathbf{x}}^{\prime }=A\mathbf{x}$
where
$A=\left[\begin{array}{ccc}a& 0& 4\\ -1& -1& 0\\ -2-a& 0& -3\end{array}\right]$
In what interval of a is the system asymptotically stable, and for what value of a is the system stable/unstable if such a case even exists?
Attempt
For a system to be asymptotically stable the real part of all eigenvalues must be negative.
$\mathrm{\Re }(\lambda )<0,\text{for all}\lambda$
Since we are dealing with a $3\times 3$ matrix, I used maple to find the eigenvalues from the system matrix. I also tried to use Maple to solve the inequality case for the eigenvalues, but I don't think I'm getting correct results.
The results I get from Maple state that the system is asymptotically stable when
$-8<a\le 5-4\sqrt{3}$
I spoke with my peers, and they said that this interval of a is wrong. Can anyone see what is going wrong?

Graph the solution set of system of inequalities:
${\displaystyle x\ge 0,y\ge 0,3x+y\le 9,2x+3y\ge 6}$

Graph the solution set of the system of inequalities or indicate that the system has no solution.
${\displaystyle \{\begin{array}{c}y\ge x^2-4\\ x-y\ge 2\end{array}}$