We need to solve the system above by elimination, which means we need to eliminate one of the variables. The first step is to change the "-15x" on the second equation from the right to the left as shown below:
[tex]\begin{cases}5x+8y=10 \\ 24y+15x=-10\end{cases}[/tex]We then need to multiply the first equation by -3.
[tex]\begin{gathered} \begin{cases}5x+8y=10\cdot(-3) \\ 24y+15x=-10\end{cases} \\ \begin{cases}-15x-24y=-30 \\ 24y+15x=-10\end{cases} \\ -15x+15x-24y+24y=-30-10 \\ 0=-40 \end{gathered}[/tex]Since the result is an invalid equation, the system is inconsistent and can't be solved.
