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Soros Olympiad in Mathematics
V Soros Olympiad 1998 - 99 (Russia)
9.3
floor + fractional parts 3x3 system (V Soros Olympiad 1998-99 Round 2 9.3)
floor + fractional parts 3x3 system (V Soros Olympiad 1998-99 Round 2 9.3)
Source:
May 25, 2024
system of equations
fractional part
algebra
Problem Statement
Solve the system of equations:
{
x
+
[
y
]
+
{
z
}
=
3.9
y
+
[
z
]
+
{
x
}
=
3.5
z
+
[
x
]
+
{
y
}
=
2.
\begin{cases} x + [y] + \{z\}=3.9 \\ y + [z] + \{x\}= 3.5 \\ z + [x] + \{y\}= 2. \end{cases}
⎩
⎨
⎧
x
+
[
y
]
+
{
z
}
=
3.9
y
+
[
z
]
+
{
x
}
=
3.5
z
+
[
x
]
+
{
y
}
=
2.
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