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How would you solve a singular matrix? ie when determinant is zero.

Lets assume an equation, (1) Ax+By=E and (2) Cx+Dy=F

if the determinant; AD-BC = 0, and therefore the matrix is singular, How to go around solving the equation?

LU decomposition, Gaussian elimination?

Ideally I am looking for a method which could be "easily" implemented in a code.

Thanks