SOLUTION: x/6+y/2+z/6=1/2 x+y+z=5 x/3+y/2+z/6=1

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Question 1097642: x/6+y/2+z/6=1/2
x+y+z=5
x/3+y/2+z/6=1
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
x/6+y/2+z/6=1/2
x+y+z=5
x/3+y/2+z/6=1
================
x+3y+z=3
x+y+z=5
2x+3y+z=6
===============
-x-3y-z=-3
2x+3y+z=6
x=3
================
6+3y+z=6; 3y+z=0,z=-3y
3+y-3y=5
3-2y=5
y=-1
(3, -1, 3)
Check
(1/2)-(1/2)+3/6=1/2 TRUE
3-1+3=5, TRUE
1+(-1/2)+(1/2)=1 TRUE

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

x/6+y/2+z/6=1/2
x+y+z=5
x/3+y/2+z/6=1

------- eq (i) ------- eq (ii) ------- eq (iii) x + 3y + z = 3 ----- Multiplying eq (i) by LCD, 6 ------- eq (iv) x + y + z = 5 ----- eq (ii) 2x + 3y + z = 6 ----- Multiplying eq (iii) by LCD, 6 ----- eq (v) =============== 2y = - 2 ----- Subtracting eq (ii) from eq (iv) =============== ----- Subtracting eq (v) from eq (iv) =============== 3 + - 1 + z = 5 ----- Substituting 3 for x, and - 1 for y in eq (ii)