In 1750 the German mathematician Gabriel Cramer published a rule for solving a set of n linear equations in n unknowns simultaneously. Consider a general system of 2 equations in two unknowns ax + by + c = 0 dx + ey + f = 0 where (ae-db)≠0 Then x = (bf - ce)/(ae - db) and y = (cd - af)/(ae - db) This can be written as with the help of determinants. Which is an equivalent solution of the simultaneous equations ax + by = -c dx + ey = -f Hence we can denote the solution as the ratio of two determinants D _{1} and D and D_{2} and D. |

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