System of linear equations

A system of linear equation is a collections of linear equation with the same set of variables.
A way to solve a system of equations is with Cramer’s rule.
To solve the 2×2 matrix:
aX+bY = c
a'X+b'Y = c'
First find the determinant:
\det=\begin{vmatrix} a & b \\ a' & b' \end{vmatrix}=ab'-a'b
If the determinant is not zero:
> \det_x=\begin{vmatrix} c & b \\ c' & b' \end{vmatrix}=cb'-c'b
> \det_y=\begin{vmatrix} a & c \\ a' & c' \end{vmatrix}=ac'-a'c
> X=\frac{ \det_x}{\det}=\frac{cb'-c'b}{ab'-a'b }
> Y=\frac{ \det_y}{\det}=\frac{ac'-a'c}{ab'-a'b}
> V = (X, Y)
If the determinant is zero (a/a’=b/b’):
> If a/a’ = c/c’: V = ((c-b*µ)/a, µ)
> else: V = ∅

Try it yourself:

X + Y =
X + Y =

Output: