Find the slope of the line and simplify the answer. -9x

Find the linear approximation of the function $f(x)=\sqrt{4-x}$ at $a=0$
Use L(x) to approximate the numbers $\sqrt{3.9}$ and $\sqrt{3.99}$ Round to four decimal places

Write and explain the three forms of linear equations.

Write the following linear differential equations with constant coefficients in the form of the linear system ${\displaystyle \dot{x}=Ax}$ and solve:
${\displaystyle \left(a\right)\ddot{x}+\dot{x}-2x=0}$
${\displaystyle \left(b\right)\ddot{x}+x=0}$
${\displaystyle \left(c\right)d\ddot{x}-2\ddot{x}-\dot{x}+2x=0}$
Hint: Let ${\displaystyle x_1=x,x_2=\dot{x}}$, etc.
I have tried to do this in the following way but I do not know if I am doing well:
Let ${\displaystyle x_1=x,x_2=\dot{x},x_3=\ddot{x},x_4=x^{\dots }}$, then the previous system becomes ${\displaystyle \left(a\right)x_3+x_2-2x_1=0,\left(b\right)x_3+x_1=0,\left(c\right)x_4-x_3-x_2+2x_1=0}$
and thus ${\displaystyle \left[\begin{array}{c}{x}_1\\ x_2\\ x_3\\ x_4\end{array}\right]=\left[\begin{array}{c}\frac{x_2}{3}\\ x_2\\ \frac{-x_2}{3}\\ 0\end{array}\right]}$. Is this what it should be or is it different? Thank you very much.

Consider a system of 2 linear equations in 3 variables.
Which of the following statements is possible?
a.The solution set of the system forms a line.
b.The system has 2 solutions.
c.The system has 1 (unique) solution.
d.The system has 3 solutions

Do the equations $5y-2x=18$
and
$6x=-4y-10$
form a system of linear equations? Explain.

a) Find a weak formulation for the partial differential equation$\frac{\partial u}{\partial t}+c\frac{\partial u}{\partial x}=0$b) Show that $u=f(x-ct)$ is a generalized solution of$\frac{\partial u}{\partial t}+c\frac{\partial u}{\partial x}=0$for any distribution $f$What i already haveI know that in order to find a weak form of a pde, we need to multiply it by a test function, then integrate it. Also, to find a generalized solution, we need to find a weak solution and just multiply it by the Heaviside function.Let's take any test function $\varphi$, then we have (integrating by parts second part of the integral)${\int }_{\mathrm{\Omega }}(\frac{\partial u}{\partial t}+c\frac{\partial u}{\partial x})\ast \varphi (x)dx=$$={\int }_{\mathrm{\Omega }}\frac{\partial u}{\partial t}\varphi (x)dx-c{\int }_{\mathrm{\Omega }}u(x,t){\varphi }^{\prime }(x)dx$where $\varphi$ vanishes at boundaries. So, is it the final form or can we proceed further? And how am I supposed to find a generalized solution?

Determine if (1,3)is a solution to given system of linear equations
$y-2x=3$
$3x-2y=5$