You have to graph the functions first.
If they intersect, they have a solution, if they do not intersect, then there is no solution for the equation system.
[tex]\begin{gathered} -\frac{2}{3}x-7y=6 \\ x+3y=-9 \end{gathered}[/tex]
These equations intersect only onece at coordinates (-9,0), this is the only point that is true for both equations.
[tex]\begin{gathered} -\frac{2}{3}x-7y=6 \\ -7y=6+\frac{2}{3}x \\ y=-\frac{6}{7}-\frac{2}{21}x \end{gathered}[/tex][tex]\begin{gathered} x+3y=-9 \\ 3y=-9-x \\ y=-3-3x \end{gathered}[/tex]
