In order to solve the system using substitution, we can use the value of x from the second equation in the first one. So we have:
[tex]\begin{gathered} \frac{1}{2}x-\frac{1}{3}y=5 \\ \frac{1}{2}(\frac{2}{3}y+10)-\frac{1}{3}y=5 \\ \frac{1}{3}y+5-\frac{1}{3}y=5 \\ 5=5 \end{gathered}[/tex]Since the final sentence is true, we have an infinite number of solutions for this system, therefore the correct option is C.
