Question

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

Answer 1

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

⇒ x+z = 2+y [from equation - 3]

x+y+z = 6
2+y+y = 6
2y = 6-2
2y = 4
y = 2

x+z = 2+2 = 4

[equation-2]
x-2y+3z = 6
x - 2(2) + 3z = 6
x + 3z = 10

subtract :
x+3z = 10
x + z = 4
_______
2z = 6
z = 3

⇒ x+z = 4
x+3 = 4
x = 1

∴ x = 1,y = 2,z = 3

Answer 2

Given Equation is x + y + z = 6  ----- (1)

Given Equation is x - 2y + 3z = 6 ---- (2)

Given Equation is x - y + z = 2  ----- (3)


1st let's solve (1) & (3), we get

x + y + z = 6

x - y + z = 2
(-)  (+)  (-)  (-)
-----------------
      2y = 4

        y = 2


Substitute y = 2 in (2), we get

x - 2y + 3z = 6

x - 2(2) + 3z = 6

x - 4 + 3z = 6

x + 3z = 10.   -------- (4)


Substitute y = 2 in (3), we get

x - y + z = 2

x - 2 + z = 2

x + z = 4   -------- (5)


On solving (4) & (5), we get

x + 3z = 10

x + z = 4
-------------

2z = 6

z = 3  


Substitute y = 2 & z = 3 in (1), we get

x + y + z = 6

x + 2 + 3 = 6

x + 5 = 6

x = 1.


Therefore x = 1,y = 2, z = 3.


Hope this helps!