There are 6 different ways to solve this system.

2x + 6y + 4z =  22
3x + 7y + 4z =  23
5x + 3y - 5z = -14

The method depends on where you are in the course.

The 6 methods are: 

1. By elimination and/or substitution
2. By getting equations in triangular form
3. By Cramer's rule, using determinants
4. By Gaussian elimination using matrices, to
   row echelon form, and back substitution.
5. By Gaussian elimination using matrices, to 
   row reduced echelon form
6. By matrices using the inverse matrix method.

The solution is (x,y,z) = (-1,2,3)

Please tell us which of the 6 methods you want us to use and
post again.

Edwin