help with determinants

Question

Did I do this correctly?

 

use determinants to dtermine the number of solutions for each of the following and DO NOT solve the systems.

 

 

a.      3x -  y =  7

        6x - 2y =  10

 

 

       3   1

                  =    6 - 6 = 0 = 0

 

       6   2

 

      answer is one solution

 

 

b.  3x - y =  -6

 

         2x  =  3y + 2

 

 

      3     1

                     =   6 - 4 = 2 ≠ 0

      3      2

 

 

     answer is no solution

 

 

thanks

Answer 1

3x - y = 7
6x - 2y = 10

For this first set the determinant is zero then there is no solution.

3x - y = -6
2x = 3y + 2

2x-3y = 2

for this second set the determinant is -7 so there is an answer for x and one for y