System of inequalities question

If possible, solve the system of linear equations in 3 variables.

a - 4b + 3c = 2
-a - 2b + 5c = 9
a + 2b + c = 6

(1) a - 4b + 3c = 2
(2) -a - 2b + 5c = 9
(3)a + 2b + c = 6
add:
(2)-a - 2b + 5c = 9
(3)a + 2b + c = 6
6c = 15
c = 15/6 or 5/2

(1)a - 4b + 3(5/2) = 2
(2)-a - 2b +5(5/2) = 9
a - 4b +15/2 = 2
-a +2b + 25/2 =9
-6b + 40/2 = 11
-6b + 20 = 11
-6b = 11 - 20
-6b = -9
b = 3/2

(1)a - 4(3/2) + 3(5/2) = 2
a - 12/2 + 15/2 = 2
2a - 12 + 15 = 4
2a + 3 = 4
2a = 1
a = 1/2

a = 12.5
b = -4.5
c = 2.5
use the matrix on a calculator and use rref to enter the matrix into.