[ [Diophantine equations in integers ]

Solve the equation $3 x+5 y=7$ in integers.

#
A particular solution to this equation is $x_{0}=4, y_{0}=-1$. According to the formula from problem $\underline{60514}$, $x=4+5 k, y=-1-3 k$, where $k$ is any integer.

## Answer

$(4+5 k,-1-3 k), k \in \mathbf{Z}$.