Question: Cramer's Rule breaks down when det(A) = 0. Example (a) has no solution while (b) has infinitely many solutions. What are the ratios x j

Cramer's Rule breaks down when det(A) = 0. Example (a) has no solution while (b) has infinitely many solutions. What are the ratios x_j = det(B_j )/det(A) in the following two cases? Bj has columns of A except the j-th column replaced with the right hand side.

(a) Parallel lines

2x + 3y = 1

4x + 6y = 1

(b) Same lines

2x + 3y = 1

4x + 6y = 2

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