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Canada Contests
Canadian Mathematical Olympiad Qualification Repechage
2011 Canadian Mathematical Olympiad Qualification Repechage
3
3
Part of
2011 Canadian Mathematical Olympiad Qualification Repechage
Problems
(1)
Solve the system of equations - [Canadian Repêchage 2011]
Source:
1/15/2011
Determine all solutions to the system of equations:
x
2
+
y
2
+
x
+
y
=
12
x^2 + y^2 + x + y = 12
x
2
+
y
2
+
x
+
y
=
12
x
y
+
x
+
y
=
3
xy + x + y = 3
x
y
+
x
+
y
=
3
[This is the exact form of problem that appeared on the paper, but I think it means to solve in
R
.
\mathbb R.
R
.
]
algebra
system of equations
algebra proposed