a) Convert the following equations into matrix: x – y = 3 2x + 3y = 1

What are the solutions to the following system of equations?
$\{\begin{array}{l}y=x^2+3x-7\\ 3x-y=-2\end{array}$

Linear systems of equations with 4 unknowns
$\begin{array}{rl}7& x+4y+3z+2w=46\\ 5& x-y+4w=23\\ & x+z=6\\ 3& x+7w=15\end{array}$

For $x^{\prime }=y$, and $y^{\prime }=-x-y$, Find all equilibrium points and decide whether they are stable, asymptotically stable, or unstable.
I found that the equilibrium points are $(0,0)$. Then I try to find the eigenvalues. The characteristic equation I found is $\lambda +{\lambda }^2+1=0$. I realize that they are complex eigenvalues...The real part of this complex eigenvalues are negative. Does this mean this is stable ? Is this also asymptotically stable? What are the differences between asymptotically stable and stable?

Solve the system of equations $2x+3y=5$
$5x-4y=2$

I have the following system of equations where the m's are known but $a,b,c,x,y,z$ are unknown. How does one go about solving this system? All the usual linear algebra tricks I know don't apply and I don't want to do it through tedious substitutions.
$\begin{array}{rl}a+b+c& =m_0\\ ax+by+cz& =m_1\\ a{x}^2+b{y}^2+c{z}^2& =m_2\\ a{x}^3+b{y}^3+c{z}^3& =m_3\\ a{x}^4+b{y}^4+c{z}^4& =m_4\\ a{x}^5+b{y}^5+c{z}^5& =m_5\end{array}$

Find all solution in $\mathbb{R}$ for the following system of equations:
$\{\begin{array}{l}x+\frac{3x-y}{x^2+y^2}=3\\ y–\frac{x+3y}{x^2+y^2}=0\end{array}$

System of ODEs with products
How can we solve the system of differential equations
${\displaystyle \frac{df(t)}{dt}}=-f(t)h(t),{\displaystyle \frac{dg(t)}{dt}}=-g(t)h(t),{\displaystyle \frac{dh(t)}{dt}}=1-(h(t){)}^2$
The system does not fall to standard ODE methods.