Integer part system

In the field of real numbers, solve the system of equations:
2x + ⌊y⌋ = 2022,
3y + ⌊2x⌋ = 2023.
(⌊a⌋ denotes the (lower) integer part of the real number a, i.e., the largest integer not greater than a., E.g., ⌊1.9⌋ = 1 and ⌊−1.1⌋ = −2.)

Final Answer:

x =  1011
y =  1/3

Step-by-step explanation:

$$\begin{gathered} 2x+\lfloor y\rfloor =2022 \\ 3y+\lfloor 2\cdot x\rfloor =2023 \\ x=1011 \\ y=\frac{1}{3}\doteq 0.3333 \\ \text{ Verifying Solution: } \\ {s}_1=2\cdot x+\lfloor y\rfloor =2\cdot 1011+\lfloor 0.3333\rfloor =2022 \\ {s}_2=3\cdot y+\lfloor 2\cdot x\rfloor =3\cdot 0.3333+\lfloor 2\cdot 1011\rfloor =2023 \end{gathered}$$

$y=1/3=\frac{1}{3}=0.3333$

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