complex Question find A, C (multiple)

I'll show you a way to solve that set of equations; there are other methods available.

1)  To make the problem easier, multiply each equation by 2:

      15a +    b  - 7c  =  13

        5a -   6b + 8c  =  10

        3a - 10b + 4c  =  -22

2) Eliminate one of the variables; I'm going to choose to eliminate 'a'.

    Take the first two equations;                    Take the first and the last equation;

    leave the first one alone;                          leave the first one alone;

    multiply the second one by -3:                  multiply the last one by -5:

    15a +    b  - 7c  =  13                              15a +     b  - 7c  =  13

   -15a +18b - 24c  = -30                            -15a + 50b - 20c  =  110

   Add down the columns:                            Add down the columns:

             19b - 31c  =  -17                                       51b - 27c  = 123

3)  Combine these two equation together:

     19b - 31c  =  -17   -->  multiply by 51:      969b - 1581c  =  -867   

      51b - 27c  = 123   -->  multiply by -19:   -969b  + 513c  =  -2337

                         Add down the columns:                   -1068c  =  -3204

                         Divide by -1068:                                     c  =  3

4)  Substitute this value (c = 3) into the equation  19b - 31c  =  -17  to find the value          for b:

      19b - 31(3)  =  -17   --->  19b  =  76   -->   b  =  4

5)  Substitute these values (b = 4 and c = 3) into the equation 15a + b - 7c  =  13              to find the value for a:

     15a + (4) - 7(3)  =  13   -->  15a  =  30   -->  a  = 2

I'm hoping that someone else can give you an easier solution to your problem.