Question

Is there a good way to solve this system of equations:
xy + yz = 9; xz + yz = 8; xy + xz = 5?

Answer 1

I notice that it can be rewritten as:
y(x + z) = 9
z(x + y) = 8
x(y + z ) = 5
But I can't find any rational way to solve this.

Answer 2

add them all
2(xy+yz+xz)=9+8+5=22
xy+yz+xz=22/2=11
now subtract each eq. from this

Answer 3

If I may help?

Answer 4

i give you hint
xy+yz+xz-(xy+yz)=11-9=2
xz=2
similarly yz and xy
ten multiply them all
xy*yz*xz=?
(xyz)^2=?
xyz=?
now divide one by one
e.g.,
(xyz)/(xy)=?
z=?
similarly other values.

Answer 5

I just guest!!

xy+yz =9 , hence y ( x+z) = 3*3
Assume y = 3, then x + z= 3

for the last one, x(y+z) =5 = 1*5, then assume x =1, then y+z =5, hence z =2

Replace all back, I see (1, 3, 2) satisfies all three equations. :)