System of two Linear Equations, presented in most general form as:

A1X + B1Y = C1
A2X + B2Y = C2

has a symbolic solution using Determinant (Det) as following:

Det =   A1* B2 - A2* B1 

X = ( B2* C1 - B1* C2 ) / Det
y = ( A1* C2 - A2 * C1) / Det

If Det=0 there is no solution.
If C1 = C2 = 0, then the trivial solution will be: X = Y = 0.

Usage Notes. If any of Text Boxes A1, A2 or B1, B2 are left empty, system will automatically assign number 1 to corresponding coefficients.