Given:
[tex]\begin{gathered} 5x+3y=-12\ldots\ldots\ldots\ldots(1) \\ 5x+3y=9\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]To solve for x and y:
Subtract (2) from (1) we get,
[tex]0=-21[/tex]But, we know that,
[tex]0\ne-21[/tex]So, the system has no solutions.
Then, the graph is,
Since the lines are neither intersecting nor coinciding lines.
Therefore, it has no solution.