An alternate way of solving simultaneous equations is throug

An alternate way of solving simultaneous equations is through the of Cramer\'s Rule which solves for the variables by taking the ratio of two determinants. The denominator is the determinant of a matrix consisting of all of the coefficients of the variable in variable order. The numerator is the determinant of the same matrix with the exception of the column of the coefficients being solved for is replaced with the constants of each of the equations in order. For a 3 by 3 system of linear equation of the form a_1 x + b_1 y + c_1 z = d_1 (1) a_2 z x + b_2 y + c_2 z = d_2 (2) a_3 x + b_3 y + c_3 z = d_3 (3) Cramer\'s rule gives the solution as follows x = D_x/D, y = D_y/D and z = D_z/D where D_3 D_x3 D_y and D_z are determinants defined by D = (a_1 a_2 a_3,b_1 b_2 b_3,c_1 c_2 c_3), D_x = (d_1 d_2 d_3,b_1 b_2 b_3, c_1 c_2 c_3) D_y = (a_1 a_2 a_3,d_1 d_2 d_3,c_1 c_2 c_3), D_z = (a_1 a_2 a_3,b_1 b_2 b_3,c_1 c_2 c_3) Solve the equations in problem 1 using Cramer\'s Rule

Solution

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