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The system of equations
x+by=-1
2ax+2y=5
is equivalent to the matrix-vector equation Ax=b, where A = matrix(2,1,(1,b,2a,2)), x = (x,y) and b = (-1,5). This equation has a unique solution exactly when det(A) is non-zero.
Now, det(A) = 2-2ab, which is nonzero precisely when ab != 1.
