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Israel National Olympiad
2024 Israel National Olympiad (Gillis)
P1
P1
Part of
2024 Israel National Olympiad (Gillis)
Problems
(1)
Symmetric system of specifications
Source: 2024 Israel National Olympiad (Gillis) P1
12/7/2023
Solve the following system (over the real numbers):
{
5
x
+
5
y
+
5
x
y
−
2
x
y
2
−
2
x
2
y
=
20
3
x
+
3
y
+
3
x
y
+
x
y
2
+
x
2
y
=
23
\begin{cases}5x+5y+5xy-2xy^2-2x^2y=20 &\\ 3x+3y+3xy+xy^2+x^2y=23&\end{cases}
{
5
x
+
5
y
+
5
x
y
−
2
x
y
2
−
2
x
2
y
=
20
3
x
+
3
y
+
3
x
y
+
x
y
2
+
x
2
y
=
23
algebra
system of equations
national olympiad