Question 1029154
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Hi, Can anyone solve this problem? The sum of three numbers is 9. The first minus the second, plus the third is 3. 
The first minus the third is 1 more than the second.  What are the numbers?
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What you are given is 

x + y + z = 9,    (1)
x - y + z = 3,    (2)
x - z = y + 1.    (3)

Modify (3):

x - y - z = 1.    (3')

Add equations (1) and (3') (both sides). You will get

2x = 9 + 1,   or   2x = 10,   hence,   x = {{{10/2}}} = 5.

Add equations (1) and (2). You will get

2x + 2z = 12.      (4)

Since x = 5, it gives 2*5 + 2z = 12,   or   2z = 12 - 10,   or 2z = 2,   and then  z = 1.

Finally, from (1) y = 9 - x - z = 9 - 5 - 1 = 3.

<U>Answer</U>.  x = 5,  y = 3  and  z = 1.

Check it yourself.
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