USAGE
Enter coefficients in input boxes  it could be any combination of Decimals, Fractions and Mixed Numbers,
positive or negative, then click on [SOLVE] button to get a solution for X, Y as Fractions and equivalent Decimals.
Following rules apply:

If any of A1, A2, B1, or B2 are empty, system will assign 1

If any of C1 or C2 are empty, system will assign 0
ABSTRACT
A_{1}X + B_{1}Y=C_{1}
A_{2}X + B_{2}Y=C_{2}
has a solution using Determinant (Det)
Det= A_{1}B_{2}A_{2}B_{1}
X = (B_{2}C_{1}  B_{1}C_{2})/Det
y = (A_{1}C_{2}  A_{2}C_{1})/Det
If Det=0 there is no solution.
If C_{1}=C_{2}=0 then trivial solution: X = Y = 0.