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Greece Junior Math Olympiad
2017 Greece Junior Math Olympiad
2
2
Part of
2017 Greece Junior Math Olympiad
Problems
(1)
Solve the system
Source: Archimedes 2017
3/5/2017
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
is positive. Solve:
{
x
(
6
−
y
)
=
9
y
(
6
−
z
)
=
9
z
(
6
−
x
)
=
9
\begin{cases}{x\left( {6 - y} \right) = 9}\\ {y\left( {6 - z} \right) = 9}\\ {z\left( {6 - x} \right) = 9}\end{cases}
⎩
⎨
⎧
x
(
6
−
y
)
=
9
y
(
6
−
z
)
=
9
z
(
6
−
x
)
=
9
function
algebra
inequalities