Use cramer's rule to solve x_1+2x_2=5 -x_1+x_2=1

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 the general forms of the equations of the lines that pass through the point and are (a) parallel to the given line and (b) perpendicular to the given line. Point (−1, 0) Line y=-3

The table shows the number y of muffins baked in x pans. What 1s the missing y-value that makes the table represent a linear function?

For the given a system of linear equations
4x+y-5z=8
-2x+3y+z=12
3x-y+4z=5
Use matrix inversion to solve simultaneous equations.

What I wanted to ask was , given a homogeneous system of n variables , like this having 4 variables:
${\displaystyle a_{1}x+a_{2}y+a_{3}z+a_{4}w=0}$
${\displaystyle a_{2}x+a_{3}y+a_{4}z+a_{1}w=0}$
${\displaystyle a_{3}x+a_{4}y+a_{1}z+a_{2}w=0}$
${\displaystyle a_{4}x+a_{1}y+a_{2}z+a_{3}w=0}$
Here , as we know that this system has zero solution and we can see that the coefficients are rotating in each of the linear equation .
So , is there any general form for solution of this system other than the zero solution ?
Also , what if we are given the non-zero solution then can we find the values of
${\displaystyle (a_1,a_2,a_3,a_4)}$

How do I craft a linear equation so that it is in the form of ${\displaystyle ax+bx+c=0}$ where ${\displaystyle a^2+b^2=1}$ if I have two points? I know how to get it into the form ax+bx+c=0 but I can't figure out the algorithm for satisfying the second condition.

The reduced row echelon form of a system of linear equations is given.Write the system of equations corresponding to the given matrix. Use $x,y$; or $x,y,z;$ or $x_1,x_2,x_3,x_4$ as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution.
$[1,0;1,0;5,-1]$