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Question 265645: what is the best way to solve this problem
3x+y+2z=31
x+y+2z=16
x+3y+2z=25
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! what is the best way to solve this problem?
3x + y + 2z = 31
x + y + 2z = 16
x + 3y + 2z =25
Elimination would be pretty easy here
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Subtract the 2nd equation from the 1st equation
3x + y + 2z = 31
x + y + 2z = 16
-------------------Subtraction eliminates y and z, find x
2x = 15
x = 7.5
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Subtract the 2nd equation from the 3rd equation
x + 3y + 2z = 25
x + y + 2z = 16
-------------------Subtraction eliminates x and z, find y
2y = 9
y = 4.5
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Find z by substitution in the 1st equation
3(7.5) + 4.5 + 2z = 31
22.5 + 4.5 + 2z = 31
27 + 2z = 31
2z = 31 - 27
2z = 4
z = 2
:
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Check solutions in the 2nd equation
x + y + 2z = 16
7.5 + 4.5 + 2(2) = 16
12 + 4 = 16; confirms our solutions
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