SOLUTION: Solve the system of equations (x+y)(x+y+z)=66 (y+z)(x+y+z)=99 (z+x)(x+y+z)=77

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Question 696814: Solve the system of equations
(x+y)(x+y+z)=66
(y+z)(x+y+z)=99
(z+x)(x+y+z)=77
Answer by god2012(113) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
(x+y)(x+y+z)=66----------------------------------------eq.1
(z+y)(x+y+z)=99----------------------------------------eq.2
(z+x)(x+y+z)=77----------------------------------------eq.3
Solution : Add all 3 equations
%28x%2By%29%28x%2By%2Bz%29%2B%28x%2By%29%28x%2By%2Bz%29%2B%28z%2Bx%29%28x%2By%2Bz%29=242
%28x%2By%2Bz%292%28x%2By%2Bz%29+=+242
%28x%2By%2Bz%29%5E2+=+121+=+11%5E2
x+y+z = 11 -------------------------------------------eq.4
substitute eq.4 in eq. 1 , eq.2 and eq.3 , we get
x+y = 6------------------------------------------------eq.5
y+z = 9------------------------------------------------eq.6
x+z = 7------------------------------------------------eq.7
Add eq.5 and 6, we get
x%2B2y%2Bz+=+15---------------------------------------eq.8
Subtract eq.4 from eq.8, we get
y = 4 --------------------------------------------------a
Put a in eq.5 and eq.6, we get,
X = 2 , Z = 5, Y = 4