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1
2013 HMMT Algebra #1: System of Equations
2013 HMMT Algebra #1: System of Equations
Source:
February 16, 2013
HMMT
Problem Statement
Let
x
x
x
and
y
y
y
be real numbers with
x
>
y
x>y
x
>
y
such that
x
2
y
2
+
x
2
+
y
2
+
2
x
y
=
40
x^2y^2+x^2+y^2+2xy=40
x
2
y
2
+
x
2
+
y
2
+
2
x
y
=
40
and
x
y
+
x
+
y
=
8
xy+x+y=8
x
y
+
x
+
y
=
8
. Find the value of
x
x
x
.
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