SOLUTION: Solve the following system of equations by any method. x/6 +y/2+ z/6 =1/2 x+y+z=5 x/3 +y/2 +z/6= 1

Question 1097690: Solve the following system of equations by any method.
x/6 +y/2+ z/6 =1/2
x+y+z=5
x/3 +y/2 +z/6= 1
Found 2 solutions by greenestamps, Jeetbhatt10th:
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

There are dozens of different paths you could take to solve this system of equations....

I would be inclined to clear fractions in the first and third equations, since working with fractions always slows things down and makes it easier to make careless mistakes. So

(1)
(2)
(3)

Comparing (1) and (3) immediately gives us x=3; comparing (1) and (2) yields 2y=-2, so y=-1. Then substituting x=3 and y=-1 in (2) gives us z=3.

Answer: (x,y,z) = (3,-1,3)
Answer by Jeetbhatt10th(11) (Show Source): You can put this solution on YOUR website!
x/6+y/2+z/6=1/2
Taking lcm,
(x+3y+z)/6=1/2
x+3y+z=3.. (1)
x+y+z=5.. (2)
Subtracting (2) from (1) ,we get
X+3y+z-x-y-z=3-5
2y=-2
Y=-1.. (3)
Substituting (3) in (1),we get,
x+3 (-1)+z=3
x-3+z=3
x+z=6.. (4)
Since x/3+y/2+z/6=1
=> (2x+3y+z)/6=1
2x+3y+z=6.. (5)
Substituting (3)in (5),we get
2x-3+z=6
2x+z=9.. (6)
Subtracting (4)from (6) we get
2x-x+z-z=9-6
x=3.. (7)
Substituting (7) in (4)
3+z=6
z=3
Hence,x=3,y=-1,z=3 (Answer)😊
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