Question 265645
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
:
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
:
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
:
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
:
:
Check solutions in the 2nd equation
x + y + 2z = 16
7.5 + 4.5 + 2(2) = 16
12 + 4 = 16; confirms our solutions