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Soros Olympiad in Mathematics
IV Soros Olympiad 1997 - 98 (Russia)
11.12
4x4 non liear parameter system (IV Soros Olympiad 1997-98 R3 11.12)
4x4 non liear parameter system (IV Soros Olympiad 1997-98 R3 11.12)
Source:
June 2, 2024
system of equations
algebra
parameter
Problem Statement
Find how many different solutions depending on
a
a
a
has the system of equations :
{
x
+
z
=
2
a
y
+
u
+
x
z
=
a
−
3
y
z
+
x
u
=
2
a
y
u
=
1
\begin{cases} x+z=2a \\ y+u+xz=a-3 \\ yz+xu=2a \\ yu=1 \end{cases}
⎩
⎨
⎧
x
+
z
=
2
a
y
+
u
+
x
z
=
a
−
3
yz
+
xu
=
2
a
y
u
=
1
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