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Soros Olympiad in Mathematics
III Soros Olympiad 1996 - 97 (Russia)
10.5
\frac{x+y}{1+xy}=\frac{1-2y}{2-y} (III Soros Olympiad 1996-97 R1 10.5)
\frac{x+y}{1+xy}=\frac{1-2y}{2-y} (III Soros Olympiad 1996-97 R1 10.5)
Source:
May 29, 2024
algebra
system of equations
Problem Statement
Solve the system of equations
{
x
+
y
1
+
x
y
=
1
−
2
y
2
−
y
x
−
y
1
−
x
y
=
1
−
3
x
3
−
x
\begin{cases} \dfrac{x+y}{1+xy}=\dfrac{1-2y}{2-y} \\ \dfrac{x-y}{1-xy}=\dfrac{1-3x}{3-x} \end{cases}
⎩
⎨
⎧
1
+
x
y
x
+
y
=
2
−
y
1
−
2
y
1
−
x
y
x
−
y
=
3
−
x
1
−
3
x
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