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1999 Ukraine National Mathematical Olympiad
Problem 1
syseq, absolute value and floor related (Ukraine 1999 Grade 8 P1)
syseq, absolute value and floor related (Ukraine 1999 Grade 8 P1)
Source:
May 9, 2021
absolute value
algebra
system of equations
Problem Statement
Solve the system of equations
2
∣
x
∣
+
∣
y
∣
=
1
2|x|+|y|=1
2∣
x
∣
+
∣
y
∣
=
1
,
⌊
∣
x
∣
⌋
+
⌊
2
∣
y
∣
⌋
=
2
\lfloor|x|\rfloor+\lfloor2|y|\rfloor=2
⌊
∣
x
∣
⌋
+
⌊
2∣
y
∣
⌋
=
2
.
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