x + y + z = 6, (1)
x - y + z = 2, (2)
2x + y - z = 1. (3)
Distract equation (2) from equation (1) (both sides). You ill get
2y = 6-2 = 4 ---> y = 2.
Substitute y = 2 into equations (1) and (3). You will get
x + z = 4, (4) ( from (1) )
2x - z = -1. (5) ( from (3) )
Add equations (4) and (5). You will get
3x = 3 ---> x = 1.
Now everybody can determine z. From (4), z = 4 - x = 4 - 1 = 3.
Answer. x=1, y=2, z=3.
x + y + z = 6 -------- Considering X is same as x ------- eq (i)
x - y + z = 2 -------- Considering X is same as x ------- eq (ii)
2x + y - z = 1 ------- eq (iii)
2y = 4 ------ Subtracting eq (ii) from eq (i)
y = , or 2
3x = 3 ------ Adding eqs (ii) & (iii)
x = , or 1
1 + 2 + z = 6 ------- Substituting 1 for x, and 2 for y in eq (i)
3 + z = 6
z = 6 - 3, or 3
Solution set:
