1. The problem statement, all variables and given/known data Let the curve A + By + Cx + Dy^2 + Exy + x^2 = 0 be given. It passes through the points (x_1, y_1),...,(x_5, y_5). Determine the A, B, C, D, and E. 2. Relevant equations 3. The attempt at a solution To create the system, I plug in each x_n and y_n into the given curve equation... [1, y_1, x_1, (y_1)^2, (x_1)(y_1), (x_1)^2] [1, y_2, x_2, (y_2)^2, (x_2)(y_2), (x_2)^2] [1, y_3, x_3, (y_3)^2, (x_3)(y_3), (x_3)^2] [1, y_4, x_4, (y_4)^2, (x_4)(y_4), (x_4)^2] [1, y_5, x_5, (y_5)^2, (x_5)(y_5), (x_5)^2] But, what do I do from here? Replace a row with vector b (all 0's in this case) and solve x = determinant of new matrix/determinant of original matrix. Then repeat for each row? Does the fact that there are x^2 and y^2 in the matrix matter at all or not?