\[\left\{ \begin{matrix} 5z - 7x = 3\ \ \ | \cdot 3\ \ \ \ \ \ \ \\ 3z - 5x = 2\ \ | \cdot ( - 5) \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} 15z - 21x = 9\ \ \ \ \ \ \ \ \ \ \ \ \ (1) \\ - 15z + 25x = - 10\ \ \ (2) \\ \end{matrix} \right.\ \]
\[(1) + (2) \Longrightarrow 4x = - 1\]
\[\left\{ \begin{matrix} 4x = - 1\ \ \ \ \ \ \ \\ 3z - 5x = 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} 4x = - 1\ \ \ \ \ \ \ \\ 3z = 5x + 2 \\ \end{matrix} \right.\ \]