(1) 4x - y = 2
(2) 3y + z = 9
(3) x + 2z = 7
z is already eliminated in (1),
so eliminate z from (2) and (3)
Solve (2) for z
(2) 3y + z = 9
z = 9 - 3y
Substitute 9-3y for z in (3)
(3) x + 2z = 7
x + 2(9-3y) = 7
x + 18 - 6y = 7
(4) x - 6y = -11
Solve the system:
(1) 4x - y = 2
(4) x - 6y = -11
Solve (4) for x
x = -11+6y
Substitute -11+6y for x in (1)
4(-11+6y) - y = 2
-44+24y - y = 2
23y = 46
y = 2
x = -11+6y
x = -11+6(2)
x = -11+12
x = 1
Substitute in
z = 9 - 3y
z = 9 - 3(2)
z = 9 - 6
z = 3
(x,y,z) = (1,2,3)
Edwin
