SOLUTION: Can someone please help? I am so confused. The sum of three numbers is 8. The first number minus the second plus the third is 4. The first minus the third is 2 more than the sec

Algebra ->  Systems-of-equations -> SOLUTION: Can someone please help? I am so confused. The sum of three numbers is 8. The first number minus the second plus the third is 4. The first minus the third is 2 more than the sec      Log On


   

Question 1125747: Can someone please help? I am so confused.
The sum of three numbers is 8. The first number minus the second plus the third is 4. The first minus the third is 2 more than the second. Find the numbers.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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Can someone please help? I am so confused.
The sum of three numbers is 8. The first number minus the second plus the third is 4. The first minus the third is 2 more than the second. Find the numbers.
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first, second,third numbers
x, y, z

Second and third sentences:
system%28x-y%2Bz=4%2Cx-z=y%2B2%29

The first sentence:
x%2By%2Bz=8

system is same as system%28x-y%2Bz=4%2Cx-y-z=2%2Cx%2By%2Bz=8%29.
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system%28x=5%2Cy=2%2Cz=1%29
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Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
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x + y + z = 8     (1)
x - y + z = 4     (2)
x - z = y + 2     (3)


Subtract  equation (2) from equation (1). You will get


2y = 4  ====>  y = 4/2 = 2.


Substitute y= 2 into equations  (1)  and  (3).   You will get


x + z = 6     (4)
x - z = 4     (5)


Add equations (4) and (5).  You will get


2x = 10  ====>  x = 10/2 = 5.


Substitute  x= 5  and  y= 2 into equation (1). You will get


5 + 2 + z = 8  ====>  z = 1.


Answer.  x= 5,  y= 2,  z= 1.

Solved.