We consider the following equation with unknowns $x$ and $y$ integers: $$7x - 3y = 1 \tag{E}$$
An incomplete algorithm is given below. Copy it and complete it, writing its missing lines (1) and (2) so that it gives the integer solutions $(x; y)$ of the equation (E) satisfying $-5 \leqslant x \leqslant 10$ and $-5 \leqslant y \leqslant 10$.
Variables:
X is an integer
Y is an integer
Start:
For X varying from $-5$ to 10
(1) \ldots
(2) \ldots
Then Display X and Y
End If
End For
End
a. Give a particular solution of equation (E). b. Determine the set of pairs of integers solutions of equation (E). c. Determine the set of pairs $(x; y)$ of integers solutions of equation (E) such that $-5 \leqslant x \leqslant 10$ and $-5 \leqslant y \leqslant 10$.
We consider the following equation with unknowns $x$ and $y$ integers:
$$7x - 3y = 1 \tag{E}$$
\begin{enumerate}
\item An incomplete algorithm is given below. Copy it and complete it, writing its missing lines (1) and (2) so that it gives the integer solutions $(x; y)$ of the equation (E) satisfying $-5 \leqslant x \leqslant 10$ and $-5 \leqslant y \leqslant 10$.
\begin{center}
\begin{tabular}{|l|}
\hline
Variables: \\
X is an integer \\
Y is an integer \\
Start: \\
For X varying from $-5$ to 10 \\
(1) \ldots \\
(2) \ldots \\
Then Display X and Y \\
End If \\
End For \\
End\\
\hline
\end{tabular}
\end{center}
\item a. Give a particular solution of equation (E).\\
b. Determine the set of pairs of integers solutions of equation (E).\\
c. Determine the set of pairs $(x; y)$ of integers solutions of equation (E) such that $-5 \leqslant x \leqslant 10$ and $-5 \leqslant y \leqslant 10$.
\end{enumerate}