SOLUTION: A) given that x+y=42, y+z=67 and x+z=55, find the value of x+y+z. B) hence, find the values of x, y and z

Algebra ->  Equations -> SOLUTION: A) given that x+y=42, y+z=67 and x+z=55, find the value of x+y+z. B) hence, find the values of x, y and z      Log On


   

Question 1116924: A) given that x+y=42, y+z=67 and x+z=55, find the value of x+y+z.
B) hence, find the values of x, y and z
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.x%2By=42
2.y%2Bz=67
3.x%2Bz=55
Adding them all together,
x%2By%2By%2Bz%2Bx%2Bz=42%2B67%2B55
2x%2B2y%2B2z=164
x%2By%2Bz=82
.
.
.
From 3,
z=55-x
Substituting into 2,
y%2B%2855-x%29=67
4.-x%2By=12
Adding 1 and 4,
x%2By-x%2By=42%2B12
2y=54
Solve for y then use the other equations to solve for x and z.